Endurance is a stat that determines if a creature can use certain abilities or not. Endurance is only used by triggered abilities like assassinate and quill burst; passive abilities like regeneration do not use endurance. The endurance appears as a blue bar below the creature's health. When a triggered ability is used, it uses up a portion of this bar; if the bar is too low, you will not be able to use the ability.
Endurance recovers steadily over time, and creatures are generated with only partially filled endurance bars. The high endurance ability allows the creature to regenerate endurance faster; other than that, there is no way to manipulate the endurance regeneration speed aside from triggers.