The number on the top right corner of a bird's portrait is what we call the bird power. This number is a combination of the slingshot bonus, hats bonus, and the bird (or card) level. To see the bird level, tap on a bird, and on the left side is shown the bonus received from each source. The number next to the icon of a card is the bird level, and that is what is used for the "Level all birds to ___!" feat.