It's probably the way it lets you use your imagination and
encourages creativity. A bit like the voiceover says in one of the Minecraft
ads: No one can tell you what you can and can't do. It's also unusual in having
two very different modes; there is the survival mode, which is more like other
computer games where you have to overcome difficulties and 'dangers' (but also
quite creative in that you have to keep finding new ways to survive, not just
avoid dangers or 'kill' enemies and the original creative (classic) mode,
where you have the freedom to create whatever environment appeals to you. All
this means that the game can appeal to a very wide market.

Another thing that makes the game addictive is that, even though you are
creating a complete fantasy world, it feels real, because of the graphics and,
as some players say, because you can come back to your 'creation' and carry on
with it any time, so people get involved in it as if it were a real building or
project.
You can try Minecraft here.