I don’t know the actual reason for doing this, but if you want to use it as a pre-check for, say, login names oder user nicknames, I’d suggest you enter the characters yourself and don’t use the whole ‘alpha’ characters you’ll find in unicode, because you probably won’t find an optical difference in the following letters:
А ≠ A ≠ Α # cyrillic, latin, greek
In such cases it’s better to specify the allowed letters manually if you want to minimise account faking and such.
Addition
Well, if it’s for a field which is supposed to be non-unique, I would allow greek as well. I wouldn’t feel well when I force users into changing their name to a latinised version.
But for unique fields like nicknames you need to give your other visitors of the site a hint, that it’s really the nickname they think it is. Bad enough that people will fake accounts with interchanging I and l already. Of course, it’s something that depends on your users; but to be sure I think it’s better to allow basic latin + diacritics only. (Maybe have a look at this list: Latin-derived_alphabet)
As an untested suggestion (with ‘-’, ‘_’ and ‘ ’):
/^[a-zA-Z\-_ ’'‘ÆÐƎƏƐƔIJŊŒẞÞǷȜæðǝəɛɣijŋœĸſßþƿȝĄƁÇĐƊĘĦĮƘŁØƠŞȘŢȚŦŲƯY̨Ƴąɓçđɗęħįƙłøơşșţțŧųưy̨ƴÁÀÂÄǍĂĀÃÅǺĄÆǼǢƁĆĊĈČÇĎḌĐƊÐÉÈĖÊËĚĔĒĘẸƎƏƐĠĜǦĞĢƔáàâäǎăāãåǻąæǽǣɓćċĉčçďḍđɗðéèėêëěĕēęẹǝəɛġĝǧğģɣĤḤĦIÍÌİÎÏǏĬĪĨĮỊIJĴĶƘĹĻŁĽĿʼNŃN̈ŇÑŅŊÓÒÔÖǑŎŌÕŐỌØǾƠŒĥḥħıíìiîïǐĭīĩįịijĵķƙĸĺļłľŀʼnńn̈ňñņŋóòôöǒŏōõőọøǿơœŔŘŖŚŜŠŞȘṢẞŤŢṬŦÞÚÙÛÜǓŬŪŨŰŮŲỤƯẂẀŴẄǷÝỲŶŸȲỸƳŹŻŽẒŕřŗſśŝšşșṣßťţṭŧþúùûüǔŭūũűůųụưẃẁŵẅƿýỳŷÿȳỹƴźżžẓ]$/.test(myString)
Another edit:
I have added the apostrophe for people with names like O’Neill or O’Reilly. (And the straight and the reversed apostrophe for people who can’t enter the curly one correctly.)