Endless world makes for addicting gameplay.
In Minecraft, your game begins in a nearly infinite world (almost 8x as large as Earth's surface, according to the website) around mid-morning. You have the day to collect the necessary supplies to make a shelter before nightfall, when dangerous creatures spawn. Once you've figured out how to make it through the night, what you make of the open-ended gameplay is up to you.
What makes this particular sandbox-style game so addicting is its simplicity. Really, all you do is survive, explore, collect raw materials, and then use them to build simple tools and structures. Even the graphics, though 3-D, are essentially 16-bit (although the landscape is surprisingly beautiful). But the open-ended gameplay and lack of any real end to the exploration will keep you playing for hours from the start.
The biggest part of the game is its namesake, mining. Once you've discovered a cave, you'll likely discover many more connected to it, and probably spend much of your time exploring. The point of all this exploration is to discover the raw materials you'll need to build in the game. Stone, wood, and coal will get you through the night, but if you really want to make the most of everything Minecraft has to offer, you'll need to find plenty of iron and other minerals. However, I've found that most of the mining I do is just excavation - not an effort to collect anything, but to carve out rooms, new entryways, staircases, etc. in my base. You can spend a great deal of time sculpting your world to your liking, as there is virtually no limit as to where you remove and place blocks (although the world is not vertically infinite).
There is also a prominent element of survival, as you have to protect yourself from hostile mobs (mobs are the creatures - there are neutral mobs like cows and chickens that do no damage, and hostile mobs like zombies and spiders that can attack). Materials you collect can be used not only for tools, decor, transportation, and mining, but also as armor and weapons. As you progress, you'll be able to create stronger weapons and armor, and the hostile mobs will become less and less of a threat. Note, however, that you can change the game difficulty to "Peaceful" to eliminate this aspect and focus solely on expansion.
As the game is still under development, there are occasionally some small glitches and oddities (for example, if you turn music on, it plays for a few minutes at a time, every hour or so). However, the controls (typical first-person - move with arrows/ADWS, aim with mouse) and ultimately the overall gameplay are unaffected.
It may not sound like much, but the game is truly very well done and a pleasantly addicting addition to any gamer's collection.