Abilities are powers that can be used by the player to temporarily increase some statistics such as running, swimming, jumping, or the amount of hearts.
You can find them in the Skills tab on your profile. Click and drag your ability to the action bar to use it. You can get the skills through various means including Shops, Quests and even by collecting certain Exploration Tokens.
There are also Class Abilities that can only be learned by reaching certain levels and after choosing a class and completing a line of missions, see Classes for more detailed information.