Your aim in Blocksum is to make all the blocks that appear on each level disappear. But, as you see from the beginning, each of these blocks comes with a number.
The gameplay is simple: to make all the blocks containing a certain number disappear, you'll need at least the same number of blocks as the ones you want to get rid of. You can join blocks with the mouse and make bigger blocks, but you should only do that if you know you'll be able to break them.
For example, you can create an enormous block of 12 or 13, but you'll be in a really, really bad spot when you go to get rid of it. You can create lots of blocks of three, though, and try to get rid of them all at once to get more points.
Blocksum is a puzzle game that, thanks to its mathematical twist, succeeds in offering an experience that's very different from most other games in this genre.