The question comes up here from time to time. See, for example:

Help: Whack-fol-the-diddle et al.
meaning - musha ring dumma do dumma da
Origins: Musha ringum duram da...
Diddle-e-i-di-di - WHY?

On the whole, the same answers come up each time; though there are always a few people with pet theories ranging from fairly sensible to barking mad, so treat it all with caution. Although there are special cases ('Shule Aroon' is one) most of what looks like nonsense now started out as nonsense (or, if you prefer, meaningless vocables) - spend some time looking through collections like Bodleian Library Broadside Ballads, for instance, and you'll see what I mean.

As for why; well, much of the time it's just because that's one of the formulae people used when writing songs intended for the popular market, some of which we now think of as 'folk songs'. As Richard Bridge pointed out earlier (if a little cryptically) it still is.