It makes them a lot easier to catch and move around where you want them to. Like, out of the vegetable garden, or to where you want to milk them.
Here's a little video I took last year while we were doing some emergency milking. This goat (called 'Naked'...) had a new-born which was only drinking from one side so we had to milk out the other side. But the goats didn't know us and this one was a bit anxious about being caught by a stranger. Without the collar, things could have gotten a lot more interesting!