Apparently my weapons officers have been leveling up and gaining skills, but I have no idea what they do. When I clicked on one of them one time, it seemed to cause my weapon officer's health to drop. Are there any explanations of these skill icons? This is for the android version if that matters.
If you click on the crew member, you should see a "Details" button. From there, you can click the "Skills" button to see what skills that crew member has. Clicking on the listed skills should give you a description of what they do.
Unfortunately the game doesn't provide descriptions for skills not yet earned. If you want to know what skills you can get, they are:
(Level 30 currently seems to be the maximum attainable, even though there are slots for levels 40-100. All of those ones use the same icon, though, which presumably is a placeholder.)