(Note: Ignoring the use of mods in this review as the near unlimited potential they bring would result in this review being a tome of impossible proportions. Go get the mods yourself and test them you lazy gits)
Cast your mind back up to 100 years ago, maybe a little bit longer and recall if you can of an innocent time, a time of putting brightly coloured bricks together on top of each other and seeing your imagined construct in the worst possible combination of bricks and pieces and claiming "it's a gun" when it looks more like the mutual union of a cow and pig, in the same way that cars crashing together at 100mph can be considered a "union" of cars. That was Lego, you made most of it and your imagination took the rest of it to higher levels of realisation for you, just you, and certainly not anyone else that saw what you'd made.
Minecraft is effectively, a 3D world of Lego with some extras tacked on such as having to go out and dig up your Lego bricks, combining different bricks together to make more things and killing things to get their bricks and such. Though I'm really underselling this one on an overly tortured metaphor that should have been put to rest after the first sentence, instead of trailing on for another 2 paragraphs.
For a definition of the game, try "Wide Open Sandbox Game" with the words "Wide Open" being wider and open than the legs of the Whore of Babylon. This game is huge, potentially. You're given the basic tour of duty in a tutorial (if you want it) before a world is generated around your starting point (or a specific amount of world on platforms where the memory size of the game is a limitation. From here you're expected to begin a life of collection blocks from various biomes (grass, mushroom, desert etc) and combine them in inventive ways to be able to go on and develop better blocks, weapons, tools and engineering machinery to be able to continue living in the world that generates while you move around.
The game's scope is enormous, reaching in size to be whatever the available hard disk is on PCs and in some cases has been calculated to be 5-6 times bigger than the Earth, you'll never be running short on the basic blocks. Where in you can find and locate all manner of blocks from wood to earth, rocks and stone to lava, rare metals and precious stones all of which lead to the crafting and manufacturing of swords, armour, picks, shovels, explosives, hoes, ladders, rail tracks, cakes, and a whole plethora of other things involved in ways that most people will likely ignore. But that's all depending upon how the player wishes to play.
You could be the intrepid explorer digging through caves and valleys, seeking underground lost civilisations and looting them (Whether It Belongs In A Museum or not) you could become a farmer of crops or livestock, managing your various animals and breeding them together to farm them for meat, leather, wool and so on. Create huge monuments for yourself (Most people go for a castle since it involves a lot of rocks and not much else, but then again the giant erupting golden breast mountain with lava sounds appealing, next to another one of the same size just to REALLY make other players sit up and take notice). Create monorails of train tracks with functional switching stations using the railroad blocks and plenty more.
You could also just run around killing monsters and get to the point of killing the "Boss" known as the Enderdragon and "beating" the game before returning to the world to continue being whatever it was you were being in the first place.
This huge scope is also the game's downfall depending upon the player. You NEED to set yourself a goal and make your own way towards it, you cannot rely on the game for it as it's about as open a world you can imagine in that YOU and YOUR actions are the ONLY guiding forces in the game (Until some prick joins the game and blows up your pixel-art of Custer's Last Stand, pervert), so the limit of the game aside from the various obstacles in the way, are your own imagination and understanding.
You could even build electrical circuits using Binary Logic for gates and from there (in theory at least, I've not seen it myself) build far more complicated structures up to basic rudimentary computer processors. Taking a look around other games and maps, it's possible to see some people making reproductions of famous land marks, spaceships from sci-fi films and shows in full detail, faithful reproductions of various vehicles made from plans and schematics. Some people even go so far as to build "Adventures" for others to engage in that sets up some of the more hazardous problems in the game for players to navigate, much akin to the Raiders of the Lost Ark introduction sequence.
It's entirely down to the player to decide what their objective is, how they wish to go about it and what they intend to do once they've done it. For your standard player that's hooked on FPS where you absolutely must run from A to B, stare at some special effects and then beat the level, this game is not likely to appeal to that player. This game is definitely one for those that like to be more creative, for those that enjoy seeing something tested and performed and then ultimately, succeed, before using it in a more creative fashion (fully functional drawbridges, pumping stations that generate blocks etc) budding construction artists or those seeking the idea of doing something nobody else has done before.
Before you realise it, or if you watch someone else and particularly the younger players at that, they'll be setting up rudimentary scaffolding around the structure they're creating because if they fall off whatever they're building at the time, they'll pancake on the ground, so now they're thinking along multiple lines of whether or not to build something, how to stay alive while building and the last challenge, how to get back down again without biting the big one. (Assuming of course they're not in creative mode and just fly back down again).
It's fun, it's huge, it's not going to appeal to everyone and there'll be a clear divide between the two that will play this and those that vehemently refuse to do so.