Their is no difference at all in their meaning.
We use an before words that start with a vowel sound, and a when they start with a consonant sound. The reason is very simple: the consonant ending sound of n in an helps to distinguish the two words. Otherwise, the vowel sounds would run together. It is actually very difficult to say "a hour" - your tongue gets stuck in the back of your mouth. It's much easier to say "an hour" (aNOWer).
Similarly, it is difficult for us to say "an ball" and very easy to say "a ball" (aball)
- For Teachers