You need crew to run your ship - mechanics to keep it in shape (repair if you have them, slow HP loss if you don't) and engineers to run it (your ship runs and turns slow if you don't have them) proportional to ship size, gunners to run your turrets or they don't work (amount increases with turret tech level), miners for mining turrets, pilots for fighters, boarders and defence forces for a yet to be implemented boarding mechanic, and several ranks of officers you need as your crew grows.
And finally the captain, which allows a ship of yours to be piloted by the AI when you're using another ship.
Aside from that, there are untrained and professional crew members. Untrained ones can do anything (except for certain high-ranked jobs such as high officers, captains and pilots), but at an efficiency of 1 per crew. Professionals can only do one job, but they start at 1.5 efficiency and level up to gain more efficiency as time goes on.
And if your crew doesn't get paid on time or is put in quarters that don't fit them, they grow unhappy, stop working, and eventually abandon ship.
It's not a super deep mechanic atm (though it's getting better with the recent addition of professionals, happiness and levelling), more of a requirement and money sink (and ship building thing, as you need crew quarters to house them). Though you can add more crew than needed to increase efficiency of the job done (faster repairs etc)
For reference, my battlecruiser currently has a crew of 510 or so