You simply need to keep the blocks at the bottom of the screen reach the top, but doing so can be tough. Each time you tap to remove a block, all the blocks move up one place, and so the trick is to match as many blocks of the same colour as you can. There are some power-ups on offer to provide assistance too, should you need them.
Get some friends involved in this and I reckon you'll have a great time trying to out-do one another's scores on Poptile's leaderboards. I know I did.