Talent, like Gems, improves the attributes of your champion. Unlike Gems, however, Talent improves the attributes of each champion individually using Talent Stones, which can be acquired by winning battles or through daily login. Talent Stones are not shared among champions, so if you want to increase a champion's power, you'll have to win fights with that champion!
To assign Talents to a champion, first tap "Power" on the main menu.
Then tap "Talent" at the bottom of the Power menu.
Select a champion from the row of icons at the bottom of the screen. (Note: Champions you do not currently own are displayed here as well, but their portraits will be greyed out and you will not be able to activate any of their Talents, even if you have acquired Talent Stones for that champion.)
Each Talent has a rank designated by the number of stars displayed at the bottom of its icon, and the Talents are arranged in groups according to rank. You must activate lower-rank Talents before you can activate higher-rank ones, and only one Talent of each rank can be activated at a time.
Tap the Talent you wish to activate.
Then tap the Activate button in the bottom right corner of the screen.
If you have enough Talent Stones, that Talent will be activated and its effect will be permanently applied to the champion.
If you decide you want to change the Talents assigned to your champion, you can reset them by tapping the Reset button in the upper left corner of the screen. Resetting Talents costs Crystals.
Resetting your Talents will restore all of the Talent Stones you spent on that champion. You can then use them to activate different Talents in whatever configuration you like.