Think of it as a Lego game running on Java with no rules. In multiplayer you can interact with other users and build things as your average online play. In single player you are alone in a big and eternal sandbox (random generated terrains as long as how far you travel). During day you collect as many construction blocks and items as you can, at night you use your resources to defend yourself against zombies, spiders and creepers (annoying green creatures who explode and destroy what is around when they get near you -sucks when is near your constructions-).
It gets more complex as new items you can craft are added to the game.
As a basic example in order for Gatinho to play with matches, he had to craft Flint and Steel with one Iron Ingot and a Flint. You get Flint randomly by digging Gravel blocks, but for an Iron Ingot it gets complex. First you need to grab Wood to build a Workbench, with a Workbench you can craft a Wooden Pick to collect Stone, with Stone you can craft a Stone Pick to collect Iron Ore blocks and build a Furnace, with a Furnace and Coal or Wood you can finally smelt an Iron Ore block to get an Iron Ingot.