why do golf balls have dimples?

Some of the other answers are accurate, but incomplete. In addition to providing lift and more distance, dimples also provide a more true flight path. Without dimples, balls would act somewhat like a knuckle ball and drift off line vs. giving a more boring flight trajectory. Knowing this provides one more advantage, important to skilled players: "working the ball". This means causing ball flight to fade or draw to suit the situation.

Manufacturers have made quite an art out of developing a variety of dimple patterns and shapes because these will cause balls to perform differently, thus offering the manufacturer (and player!) a competitive advantage.

a golf ball has dimples because it is more aerodynamic and does have a little to do with the rolling on the green and fairways

but a golf ball with dimples does fly farther

I won't repeat what others have said about trajectory, flight distance, and all that. Why say it again? Another reason is to provide a challenge. The spin of the ball determines whether you hook, slice, or by the grace of God, hit it straight. Without the dimples, the ball would go straight every time. You might still hit it to the left or right, but the flight path would be straight, as opposed to the curveball that a hook or slice creates.

It is strictly for cosmetic reasons. It makes the golf ball cute. As an added benefit it helps make the golf ball meet PGA specifications.

The dimples and fuzz allow the balls to curve, just like the laces do on a baseball. Controlling that curve, is what makes sports stars out of mere men!

The balls would never stop rolling especially on the greens if it weren't for the dimples.

JUST SO the ball can balance on the golf tee=D

Short Answer: Lift.

Longer Answer: It was discovered (accidentally) that rough (non-new) golf balls flew farther. Eventually they manufactured them that way.

it gives aerodynamic lift to the ball , so it travels farther

It goes through the air better?