What is Game Design? What is Player Psychology?
These two fields are infact two sides of the same coin. Game Design is the field of constructing a scenario in which the outcome is victory or defeat. It aims to produce an uncertain winner from a fixed starting point. Player Psychology on the other hand is the study of a game from the perspective of a human. It aims to view every possible game-state and examine the state of the human in that position.
The purpose of these twin excercises is the same: fun. A person aiming to be a successful game designer must attempt to maintain the goals of both fields in order to create a fun game.
Now this principle is not at all as simple as I've presented it so far, and as I'm sure you can probably tell theres hours of principles, case studies and explanations surrounding this topic so in the interests of time, and so that I dont confuse people with too much at once, I'm just going to cover the big three: choice, metagames, and perception.

On Choice:
A videogame is defined in the most basic level as the presentation of an experience, altered by the choices of its audiences. That is to say, you cannot have a game without choice, and you cannot have a choice without impact, or else you would not be creating a game. Obviously this doesn't make projects without these elements any less valid/worthy, but just...different.
Anyway: Choice. Choice is the secret ingredient to any game and all your favorites will be excellent examples of its usage, and all your least favorites will be examples of poor handling of it. 
Most often, a choice that the player feels keenly but has little impact is more dirable for the experience than a massively impactful change that the player doesn't feel as much. In Minecraft the decisions you make on how to survive the first night, or to build your amazing brige makes no difference to the game on any meaningful way, but your experience is fundamentally altered. For you this is probably something obvious that you paid no notice to, but from a designer's perspective, this is the ultimate goal. By simply providing you with a selection of tools I've created thousands of unique playthroughs without doing any extra work, and because this experience was directed by the player I dont have to motivate them.
But the secret is larger than efficiently delivering the game with the minimum development, it works into the way the game feels to the player. This is perception and we'll cover that next.
But before we do, choice has another power over the player, the personalisation of the experience. A film will be same same no matter who watches it, and with a few variations everyone will experience it in the same way too. With a game the power to direct your experience makes it inherently unique to each player. This isn't going to be a grand or philosophical point, I'm actually discussing the ability to make the world feel vibrantly alive. The suspension of disbelief is a phenomenon we're all familiar with, nobody cares if creepers are real when they're playing Minecraft. The player agrees to pretend that they do before they even begin. For both games this quality relies heavily on immersion  and in turn empathy. Empathy is your ability to place yourself into the logical and emotional perspectives of another, be them real of fictional. Without being able to position yourself into the world you could have no immersion. In Neuroscience empathy is most often found in the same locations of the brain in which the real signals would be found. When you empathise pain your pain centers activate, the same is true with curiousity, imagination, pleasure and anger. Without atleast one of these to act upon the Brain struggles greatly with immersing itself. You will notice that all these qualities are fundamental to our understanding of the world, and if we disrupt these the world begins to feel false. We live our whole lives making choices every second, and we live in a world where those choices have consequences. The proper expression of choice, in this manner and in the curiosity it generates, is the strongest provider of immersion.

On Perception:
Perception is to a game designer an eraser. You can hide flaws in your design, cracks in your concept, or use it obscure metagame (which we'll look at soon).
You see, at the end result, all a player knows is what they perceive. In our example all the player knows about their minecraft save is their experiences. Because the game doesn't allow restarting from a previous save, the player never knows what could have happened if they'd acted differently. The human brain is absolutely amazing at spotting patterns in the world, and the moment something notable occurs, like finally finishing your house, or falling into lava, your brain can and will reflect immediately on the choices that got you there, like a long string with knots on it. But crucially at each choice there is a "what-if?" A thousand small questions with unknown possibilities. We know on a purely logical level that the game probably would not have changed a great deal, but the question remains. We still question what would have happened if we'd gotten those diamonds hanging over the lava, would we have finsihed the house sooner? or perhaps we'd have mined obsidian and gone to the nether, forgetting about the house and spending months on a hell fort.
Its is that unknown, the creating of a percieved infinity that holds our attention. the beauty of this is that even once you know it's a trick, it holds no less power over you. We touched on this in the previous section on choice. I mentioned that besides choice it was the curiousity it generates that fuels immersion it is that same curiousity I'm referring to here.
But of course this is just the perception of experiences, what about the perception of mechanics? I don't really need to go much further than to say that the perception of the players is often more powerful than the idea they percieve. For an example from my own work, on the TBNR.net Minecraft minigame server is a game called SwitchUp, and this game revolves around randomised classes being given to the players: the Boomer Class on SwitchUp is the most powerful on TBNR by far with the capability to deal 295 damage every respawn, taking only 4 seconds to do so. For reference the EnderDragon has 200 health. This class doesn't feel overpowered though, and there are no forum posts calling for a reduction in its power, infact i'm more often called upon to make it more powerful, so why? 
The answer is of course perception. The player sees bright flashing TNT and the enemy sees death-in-a-box and the numbers don't matter. A careful combination of difficulty to use, communication of immediate threats and urgency remove the calculation from any players interacting with or playing as the Boomer. By Mojang and TBNR's use of perception tactics, such as the rapid placement of them, the chaotic PvP setting, and the flashing white entities, the flaw in balance and design is obscured from the player's view. It is this which allows him to exist in his current state without issue.

On Metagames:
And now onto metagames. A metagame is, as the name suggests, a deconstruction of the game in pursuit of a victory beyond that which the game presents. In many games this is the pursuit of efficiency or speed. In some iterative games like Call of Duty of Leage of Legends, it is the pursuit of consistency. Oftentimes metagames are an inevitability as players begin to explore the edges of the scenarios given to them and are forced to find new ones. This in itself is not at all a problem and a smart designer will plan around or for them, however if unchecked these will pose a massive threat to all the hard work you put into your game.
I'm going to give you two examples of metagame in minecraft, the first bad, and the second good from the perspective of the developer.
Here perception can quickly become your enemy, if an item of your game is percieved to be useless, soon the hardwork you invested in this item, the artwork, stats and so on will become wasted time as this item is untouched. Minecraft has historically done very well with this, but it wasn't always the case. Before November 2011 there was no Enchanting of items. This meant that weapons, tools and armour crafted from gold were realistic, gold is a very soft metal and not very good for any of these uses, but realism in Minecraft is pointless, what it truly meant to the players was there was no reason for gold ingots to exist at all. There wasn't a lot of cost to the game here as the tools were exactly the same in a different colour, and gold was too rare for it to matter. What happened next was an extremely clever move on the part of Mojang, as the 1.0 update meant that gold items could be enchanted and made more powerful and useful. But with the people who could build an enchantment table requiring diamonds to do so, gold needed new purpose that the usual "because its better" couldn't provide. So what did they do? they made enchantments on gold items more powerful but did not change the items themselves. Combined with a carefully laid out set of potential enchantments, this meant that a gold tool was valuable because it could be immensely specialised. A Gold Sword could be made to kill zombies faster than a diamond one, but not players. This created a new mechanic that gave utility without altering the balance unecessarily. Now crucially the metagame here didn't create the problem, Notch did when he added golden tools. The metagame exposed it, and a change in design fixed it.
But for the more positive metagames you need look no further than the community projects undertaken with this game as a platform. As I said the point here is to distill the game into components and make a new game out of them in the process. This started with challenges such as digging a hole and never resurfacing, and has progressed into projects like Forge, Feed the Beast, Bukkit and of course CogzMc's Gearz product. From there we frequently see uses like the recent construction of the country of Denmark 1:1 or in the city planning of Stockhom.