Here's what I have been taught at school: 

"an" is correct if the **next** word begins with a **vowel sound**. So, mainly a, e, i, o, or u, but not necessarily. 

Example:

 - a uncle, but an union
 - a monitor, but an MNC bank (the last one is from [here](http://www.englishrules.com/writing/2005/a-versus-an-the-indefinite-article/))

What I have also heard about: It depends on the dialect. There may be regions where "an" is commonly used, no matter how the next word begins. But of course, this has nothing to do with correct grammar.