Ships and planets get experience when doing things. Experienced units are better than inexperienced ones in certain aspects. In a nutshell:

  • Experienced units fight better
  • Experienced ships have a smaller risk of running on a mine
  • (4.0i) Ships can be given hull functions that require a particular experience level to work.

  • Ships gain experience by moving, doing alchemy, fighting, and training
  • Planets gain experience by fighting
  • Just sitting there and doing nothing also gets you a little bit experience
  • (4.0i) Academy ships can educate new crew faster than normal ships

Full details are on the Experience page.