I have always roasted my beets in a bit of vinegar in the bottom of the pan like 1/4" or so. It is how I was taught. But why do it? What does the vinegar do for the beets?
I think it is mostly for the taste. It certainly isn't necessary - I roast beets without any vinegar all the time, and they turn out great. I just roast them in their skins, without any oil or anything added. It takes a long time, over an hour depending on how big they are. When they are completely tender, let 'em cool, and the jacket slips right off. Roasting intensifies the flavor by caramelizing some of the sugars and removing moisture. You can always season with vinegar after roasting, depending on what you plan to do with them.
That's the first I've ever heard of roasting beets in vinegar.
Acids will intensify the color of anthocyanins which are the red, purple, and blue pigments in foods. For instance, sauteed red cabbage will end up a blah blue color unless you incorporate some acid (red wine, vinegar, etc.) and then it will brighten right up to a bright red/purple color.
This could be part of the reason that someone started doing it this way (whoever it was that showed you) but when the beets are whole there would be minimal contact with the vinegar so I would say it's primarily for the sweet/sour flavor contrast.
Have you asked the person that taught you to do it that way?
Vinegar does a couple of things. Taste, obviously, which is a good reason when cooking.
The acidic nature of the vinegar does have additional effects - the acid will 'cook' your beet somewhat as well.
Specifically about beets: well, they have an earthy, sweetish flavor, often. The vinegar can complement this nicely.
Thinly sliced beet (carpaccio) in vinegar can be nice enough for the beets not to require any additional treatment (read: heat).
All of the above, and one aesthetic reason: Beets and cabbage will often turn a blueish color when cooked - the acidic nature of vinegar will revive their reddish hue, making them potentially more pleasing to look at, thereby more palatable....