"Minecraft is a game about placing blocks while running from skeletons. Or something like that."
At least that's how one-man development machine Notch describes it. In effect, Minecraft is a giant, procedurally generated sandbox stuffed to the brim with resources and tools with which you can shape and sculpt the world for as long as your imagination keeps firing.
Also, there are skeletons who will attack you.
You can play an older, simpler version called Minecraft Classic for free in your browser (though you may need to install Java). In this version you are given a stack of premade blocks (from stone to glass and brick) to set about building with - no mining necessary. There are even multiplayer servers up and running if you all want to give it a go together.
I'd thoroughly recommend paying the ten Euros though and getting hold of the latest alpha version. Notch has added a raft of new features since making the browser version available and continues to roll out surprising updates each week. The latest alpha build is almost unrecognisable from Minecraft Classic.