In Icelandic, Æ is a diphthong. In Danish and Norwegian, Æ is now a unique vowel, not a diphthong, umlaut, or ligature. In German and Swedish, the letter "Ä" is the equivalent.
In Old English, the ligature was used to denote a sound intermediate between those of "A" and "E" (IPA [æ]), very much like the short "A" of ''cat'\' in many dialects of modern English. In this context, the name of the letter is Æsc (Ash in modern English, meaning the tree), after the name of the corresponding letter in the Futharc.
In Latin, the combination denotes a diphthong (IPA [ae]) that had a value similar to the long "I" in most dialects of modern English. It was used both in native words (spelled with "AI" before the 2nd century BC) and in borrowings from Greek words having the diphthong "AI" ("ΑΙ"). Both classical and modern practice is to write the letters separately, but the ligature was used in medieval and early modern writings, in part because "Æ" was reduced to a simple long vowel (IPA [e:]) in late Latin.
The symbol "æ" is also used in the International Phonetic Alphabet to denote the sound of the Old English letter, an unrounded, semi-open front vowel. In this context, it is always lowercase.
For computers, when using the Latin-1 or Unicode sets, the codes for 'Æ' and 'æ' are respectively 198 and 230, or C6 and E6 in hexadecimal.
In HTML, you can also use the HTML character entity references Æ and æ.
See also: Å, Ø, Þ, Ð, Yogh, &OElig