There is no real goal in the game. It's a _huge_sandbox, figuratively and literally

Explore the vast randomly-generated landscape, dig your shelter against the hordes of zombies and green walking penises at night, build enormous structures or houses or statues of yourself or rollercoasters with minecarts, mine for ore deep underground and upgrade your equipment with rare diamonds, go spelunking in fascinating underground cave systems full of monsters and valuable ores, etc...
The game is centered around exploring and building.
The free "classic" version is boring, you can only build structures in there. "alpha" is where development is currently happening, but it's not free. Only alpha offers monsters, mineable ores and stuff.