Pilots become more experienced as they get more levels and higher ranks: in fact pilots' levels and ranks are interrelated and complement each other. In short, 1 rank consists of 10 levels.
Levels.
By increasing your pilot' levels your pilot's most recently learnt ability gets stronger: each level increases its effectiveness by a small portion until your pilot is ready for a rank promotion.
You level up your pilots just by participating in battles: for each battle your pilots take part in they get experience points. Note: it doesn't matter whether you use all your robots or deploy only some of them in a battle—all your pilots in the hangar deck you used in battle will get experience. The number of experience points your pilots get in battle depends on honor points you managed to get and your personal league.
Alternatively, you can speed up the process and level up your pilots with Au.
All the experience points gained in battles are considered excessive if a pilot is ready to be promoted to a higher rank—they are not accumulated towards the subsequent levels.
Ranks.
As soon as your pilots hit a maximum level for a current rank, they are ready to be promoted to a higher rank with Au, i.e. every 10 levels give you an opportunity to promote your pilot to the next rank.
When a pilot is promoted to a higher rank, they learn a new random skill suited to your robot + equipment configuration. This way, a pilot with a higher rank has more skills:
Private: 1 skill available (level 1 - level 10);
Corporal: 2 skills available (level 11- level 20);
Sergeant: 3 skills available (level 21 - level 30);
Lieutenant: 4 skills available (level 31 - level 40);
Captain: 5 skills available (level 41 - level 50);
Major: 6 skills available (level 51 - level 60);
Colonel: 7 skills available (level 61 - level 70).
The greater your number of experienced pilots, the better the pilots available to hire in the Training Center.