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 and gather things like wood, stone and iron ore to begin building a proper shelter. For those who found the resource-management part of Minecraft to be a bit much, you'll likely feel more at home with Terraria, as it streamlines the process quite a bit.
For example, if you want to gather all the wood on a tree, you don't have to chop each individual portion of the tree separately; you can simply hack away at its base and the entire thing will come tumbling down. This same simplicity is carried over into the crafting menus, where a list of craftable items is presented to you, rather than forcing you to discover the right crafting combinations on your own.
Doing basic tasks like constructing buildings, defeating the various low-level monsters that roam the world and speaking to other human characters help to flesh out the world as well as open up things like new items and enemy encounters. Like Minecraft, Terraria doesn't require that you do anything, and you could quite literally play the game for an infinite number of hours doing little more than building a shelter and sitting inside of it. It's up to you to seek out things to do, and once you do a little exploring, you'll realize that the game could well suck up tens if not hundreds of your hours before you see everything it has to offer.
Despite drawing influences from a very popular title, Terraria really is its own beast, and you'd be foolish to pass it up on iOS. The Windows version of Terraria costs US$9.99, and while that alone is a bargain, the iPad cuts that price in half to $4.99. It's an absolute bargain and a gaming experience that will be unique for every single person that plays it. A must-have.