The "weird æ symbol" is what's now known as an "a-e ligature" & was once a letter of the alphabet. It occurs in many Latin words, especially those derived from Greek. "Dæmon" is the Latin version of Greek "Δαιμων" ("Daimon" with a long "o").
The word originally meant a benevolent nature spirit (see the Wikipedia article Dæmon). The normal modern English spelling "Demon" almost always signifies a malignant spirit, particularly in Judæo-Christian beliefs. The older spelling is often used to avoid the implication that the entity is necessarily evil, which the Dæmons in Doctor Who are not -- they're a species that has both good & evil individuals, just as humans do.
British English retains a number of ligatured spellings that other forms of the language (such as US English) have dropped, for example:
- archæology (US archeology),
- Judæo-Christian (US Judeo-Christian),
- fœtus (US fetus) -- this has an o-e ligature, also derived from Latin.
The spelling "Dæmon" may not, therefore, seem as unusual to the British as it does to (say) Americans.
- ↑ The Old English name of this letter was "æsc" (pronounced "ash"), because the shape of the letter resembles that of the winged seeds of the ash tree.