Fairway
The fairway is the closely mown playing corridor between the tee and the green.
The fairway is the ideal path of every hole: short mown grass on which the ball lies cleanly and is good to play. It runs from the tee towards the green and is bounded to the left and right by the rough, the higher grass. Whoever hits the fairway has the best starting position for the next shot. The width varies depending on course and hole; narrow fairways increase the difficulty significantly. Between fairway and rough there is often a semi-rough as a transition zone.
In practice the fairway hit is more important than length. An example: your drive flies 230 metres into the rough. Your fellow player plays 190 metres onto the fairway. From the short grass the second shot is significantly easier to control because no high grass comes between clubface and ball. Whoever regularly hits more fairways usually plays better scores. The safe tee shot often beats the maximum one.
One misunderstanding is the assumption that there are automatically good lies from the fairway. Even there the ball can lie in a divot scar. The rules provide no relief for that in the normal case, unless the local rule allows "preferred lies" in poor ground condition. Follow the notices in the club office, there the rule of the day stands.
FAQ
Is it more important to hit far or to hit the fairway?
For most players the fairway hit counts more than pure length. A drive of 190 metres into the short grass is better playable than 230 metres into the rough, because no high grass comes between clubface and ball. Whoever regularly hits more fairways plays the better scores according to experience.
May I lift and clean my ball on the fairway if it lies in a divot scar?
In the normal case no: a divot scar on the fairway counts as normal course condition, and the rules provide no relief for it. Only if the course management has posted preferred lies as the rule of the day in poor ground condition may you lift, clean and re-place the ball. The notices in the club office tell you what applies on that day.
Where exactly does the fairway end and the rough begin?
The fairway is bounded to the left and right by the higher mown rough, in between there is often a semi-rough as a transition zone. For the rules the boundary is secondary because both areas belong to the general area. Practically only this counts: the shorter the grass under your ball, the cleaner the contact.