@LaPorta - it's not used much at all. You'd never use it unless you were doing calligraphy or other heavily stylised text, or writing a certain type of fiction. The only usage I remember off the top of my head is dæmon, which isn't how normal people spell it. The internet tells me it is called 'ash tree'. Interested to see what cheesy says.
The forum really doesn't like long comments here. OK. Sorry @twelvetone12, wall of text incoming...
It doesn't really have a specific name (some people call it "ash", but see below), it's just a fancy way of writing 'ae' as a ligature. It's used (but isn't obligatory) when, historically, there would have been an a-e diphthong (two vowels sharing the same syllable)...
... usually in words derived from Greek or Latin. In British Modern English it's sometimes pronounced as the diphthong but mostly just as a long 'ee' (as in encyclopædia). American pronunciation of that is more flattened and consistent, and American orthography has largely (but not exclusively) settled on just 'e'. Sometimes in BritE it's written just as 'e' too. The American spelling makes more sense ...
... with way the language is actually pronounced, but I think æ is visually really pretty so I use it. And trying to make English spelling work the way it is pronounced is, at this point, a lost cause :-D.
To make this more confusing, the same character is used for something else in Old English (I mean OE in the strict sense here.) In OE it is used for 'a' as in 'cat', while 'a' is used for 'a' as in 'father'. So the name Alfred was written Ælfred. This letter was called 'ash'. It's totally separate in use from the Modern English use of æ though, so I think it's confusing to call the modern usage 'ash'.
It’s very fascinating. I was curious as to if there is a key for it, or you had to do some sort of option-key combo to type it, or if it is automatically filled in. I’m in the medical field, and always took note of other things, such as my Indian colleagues writing the letter o before words that start with e here (such as oesophagus instead of esophagus, but still pronouncing it esophagus). I love the history.