Cooldown refers to a time period that must pass before an ability can be used again. Every ability has its own cooldown.
Most abilities enter their cooldown period immediatly upon use, while in some other cases, cooldown will not start until the ability is deactivated (such as Leon'sCloaking Skin). Autoattacks don't have a cooldown and are instead affected by attack speed.
Some upgrades can reduce cooldown times as shown below.