Abilities are unique heroes' skills used in the battle. There are 5 types of abilities : Ability 1 (Basic),  Ability 2  and 3, Passive and Leadership Ability.
Each ability is unique for every hero, and has 7 levels. There are a few heroes that has 8 levels of abilities.
You can find abilities decription by opening a hero after tapping  the tab "Heroes" on the left.  
Abilities 2 and 3 has a cooldown, which means that this ability won't be available for use until  the cooldown is over.
Most heroes can cast various Buffs and Debuffs.

Please note that not all heroes has Leadership Ability, only Leaders do.
We recomend reading heroes' abilities description carefully when choosing hero, as they can play the key role in your journet to victory!