The answer to what is minecraft is fairly complicated particularly when you consider that the game itself is very simplistic and I think it varies from person to person.
I look at it more as an exploration game. I only build things that i need and spend most of my time exploring the ever expanding world. On the other hand you have another group of people that use minecraft as sort of a digital lego land. These are the guys that build the incredible buildings and other objects that really serve no purpose they just build them because they want to.
I just find it interesting that a game with no real objective can be so fun to so many people and the reasons it is fun to everyone varies.