Besides a standard level, captains also have a Star level, which grants every captain additional bonuses.

The bonuses work permanently with the captain (if the captain is active).

You can see the current Star bonuses in the captain information window. You can see other Stars levels' bonuses by hovering your mouse over the Star. 

Each Star also provides you with faction points. The number of faction points you see on every Star level is the total number of faction points you will have, including all previous Stars.

To increase the Star level, click on the arrow on the right side from the Stars.

You will see the required number of captain fragments and Essence of Immortals you need to upgrade the Star level.