The golf ball is, at its core, the counterpart of the soccer ball from the Heroic Map Pack, redesigned for Sandbox in Halo 3 and for Forge World in Halo: Reach. It looks like a normal golf ball: round and white, but much larger. If it is struck with the 7 wood or the Gravity Hammer, it will go flying. Other weapons can also push it around, albeit with a lot less strength.
The Tin Cup in Halo 3 and Reach has a magnetic effect on the ball. If the ball gets close enough (around the radius of the green), it will be pulled up to the hole in the center. The same magnetic effect will also make it harder to remove the ball.
Halo 4 and onward games with Forge do not have this magnetic effect.
In Halo 3 it is possible to control the golf ball's direction by tapping it then pressing the 'action' button.
This is because the ball is classed as a vehicle (but no prompt to roll it appears), which is also why the ball will bounce off shield doors.
In Halo 5, the Tin Cup is separated into individual objects: a flagstick, a hole cup, and several ring-shaped terrain pieces for the hole cup.