What is it?
It is your track record of completing hired contract objectives over time as well as your financial resources, ship type, and combat success. It is a rating that primarily determines your long term wealth building rate (the pay you command for your services), but can also impact what kind of costs (licenses for example) and opportunities apply for you (building crew loyalty faster for example). In the lore of the game, entities that are considering hiring you for a job consider it an indication of your potential success, hence they'll generally pay more for a pilot with a higher reputation/rating.
How do you get it?
Successfully complete contract objectives, increase your wealth, upgrade your ship frame, and destroy enemy ships.
Who gets it?
You earn it.
And where can you find it?
Same as #2: Successfully complete contract objectives, increase your wealth, upgrade your ship frame, and destroy enemy ships.