Often times the most mobile games are the most simple affairs. That's absolutely true for Threes, which has skyrocketed itself to the number one paid App spot in multiple regions. The concept is really easy to pick up -- you just flick numbered tiles across a board to "meld" numbers together and create larger ones.
So on the board above you could flick the "1" in the lower left hand corner down, then flick it to the left to "combine" it with the "2" and make a "3." You can only meld numbers together higher than 3 if they are "twins" (the same). As a tip, finding a way to combine the numerous 1s and 2s on the board as soon as possible is the key to victory, before they pile up and become unmanageable.
Basically, all you're doing is flipping numbers on a board until you get a high score, or the board fills up and you lose. Then you touch the option to start over and you keep doing it again and again. Threes is not the most amazing concept ever, but it's fun, and anyone can play it regardless of their mathematical or gaming prowess.
You can grab Threes on the App Store for $1.99.