The top-left square is yours. Just that one, to start.
Press a colour below, and two things happen: your square turns that colour, and any squares right next to yours that are already that colour join your patch.
Now your patch is bigger. Press again, and your whole patch changes colour together and grabs whatever new squares are touching its edge — spreading like spilled paint.
Keep going until the whole board is a single colour. Fewer moves, higher score.