Each hirable NPC has 7 skills and each skill has 5 levels of competency (the more stars, the better). Numbers of stars are somewhat randomly generated in that I don't think it is possible to get NPCs with really low numbers of stars any more.
Only the skills marked in bold font are relevant to the performance of the NPC in question (their Primary Skills). In most cases, each NPC will have three Primary Skills but Engineers just have one. Marine Officers are somewhat unique in that only they have a skill that improves with use, "Boarding Experience".
In Rebirth 3.00, Virtual Seminars were introduced to the game, which allow us to add a star to a Primary Skill of our hired NPC. They are available via Smalltalk from other NPCs and this feature is described in more detail in the official guide to 3.00 here and on this wiki here. Virtual Seminars cannot be used to increase a Marine Officer's Boarding Experience but since Virtual Seminars take some effort to acquire, I would suggest that would be a waste anyway.
Info on exactly how the skill values are are used is sketchy but CBJ has revealed a few titbits:
Further info on Marine Officers from w.evans:
Finally, a word on mods/extentions. There are of course a few caveats to take into conideration before using them, which are outlined here if interested. With that health warning out of the way, onto the fun stuff w.evans has put together an elegant series of scripts based around improving combat-related AI, found here and here, for in-sector and out-of-sector conditions, respectively. They interlace a bit but they're very modular even within themselves, and there's also an all-in-one-option on the Workshop. Anyway, back on topic - at their core w.evans has built a system that improves combat AI for NPCs with better skills so it gets special mention here