Having been a part of the Minecraft community since the early Alpha days I'll try to answer your questions. Now, granted I haven't been actively playing since then, and currently haven't been playing at all.
There are different types of Minecraft. There's Vanilla MC (Un-Modded) and the different Mods. In Vanilla MC you have the standard blocks entered into the game. You got a open world where you can build houses, cities, communities overall etc.. You can go on "adventures" mining for minerals. Fighting zombies.. Fighting friends etc...
When it comes to the modding there's so many things to choose from. There are mods that give you SO many more options. You can build automated systems. E.g power generation (water-plant, solar power etc). You can build an automatic farming system with the use of different types of electricity and machines that you build. Let's explain one very easy system.
Based on time (ticks, as they're known in MC) you can have a certain machine do a certain thing. Such as auto-harvesting your crops.. Your crops then float into a new system that feeds them through different pipes (tubes) into a chest. From this chest the wheat is then sent through to a new system where the wheat is turned into bread. As a final stage the bread is then sent to your storage room where you want them.
You can also make systems where you go to a machine and choose WHAT you want to get from the "storage" and the system then picks it up for you and brings it to you. Instead of having to go through all your chests, trying to find the items you were looking for etc etc...
Above all you can build the most amazing buildings etc...
---------
For me it's playing with friends. Playing the mods that allow you to do so much more. Using logic circuiting to create systems. Using the ComputerCRAFT mod to create programs inside this game. (using real programming by the way) etc etc... I do find Vanilla MC utterly boring though.