Terraria is an indie action-adventure game. You play in a randomly-generated 2D world, with a focus on exploration. You can explore the world, gather materials, construct a house, attract NPCs to live in your house, craft or find powerful weapons and fight monsters of various size, strength and absurdity.
It is an incredibly addictive game. Exploration is constantly rewarded. There are literally hundreds of different items to be found, used and crafted, such as swords, bows, guns, harpoons, magic spells, magic boots and even lightsabers.
If you get stuck on what to do, there is a helpful guide NPC standing around that you can talk to, as he always offers useful advice. The Terraria Wiki is also very helpful.
If you have a friend with the game, you can both play in the same world together. This enhances the enjoyment you can get out of the game even more, and the amount of fun to be had in singleplayer is already high enough as it is.
Terraria is a very cheap game, and when it goes on sale on Steam it can go down as low as $2.50. The hours of enjoyment you can get out of this game compared the price you pay is incredible.