The easiest way to describe Terraria would be to say that it's like a 2D version of Minecraft, but this would also be selling the game short in many regards. The familiar sandbox gameplay mechanics that the two titles share -- things like gathering resources and crafting items -- mask a much deeper game that lies just below the surface. It offers an experience that will suit a large variety of gamers thanks to the ability to play in many different ways, and progress towards your own desired goal.
When you start up Terraria you are dropped into a randomly generated world with just a few tools at your disposal and nothing in the way of shelter or supplies. You must explore your new surroundings