maga = you (singular, formal)
maga = him/her/itself (nominative)
I'm translating some stuff from this article (not the entire article, though): http://www.nyest.hu/hirek/tegezhetem-ont-a-magazas-tortenete
tegez (vkit) = to call someone "te"
magáz (vkit) = to call someone "maga"
önöz (vkit) = to call someone "ön"
The last two are often synonymous, used in the sense that "to call someone by formal pronouns", ie. "to you." The resulting nouns are tegezés, magázás, önözés, (thouing, youing.) I'm going to use these words for the sake of convenience.
Everyone tegez'd each other until the the 16.-17. century. The first step to magázás was the usage of honorary titles, such as kegyelmed (your mercy (sing.)) or nagyságotok (your greatness (pl.)) Kegyelmed became quite wide-spread for a time, you might encounter it & its derivations (kelmed, kend) in some texts (usually old or archaizing ones, folk tales & songs & from some dialectical speakers.) These forms obviously took/take third person verbs (& everything else), but at this intermediate stage, it didn't carry over to other sentences or parts of sentences. The articles example is this:
"Nagyságod írja (3rd person singular) meg, mi akaratod (2nd person singular)."
Maga comes into the picture when the phrase "maga kegyelmed" (your mercy itself or itself your mercy, unless my intuation betrays me) (widely used then) shortened to maga/maguk. This usage wasn't symmetrical, the superior magáz'd the inferior, so it could be rude to magáz someone (the very last part is true nowadays too.)
Ön was a conciously coined term during the era of that one big language reform we had (nyelvújítás, from the late 18th century to the early 19th century.) It comes from önmaga (another word meaning him/her/itself), it just loses the -maga part. This period of the language is extremely interesting, literature-wise it's rivalled only by the time dominated by the journal Nyugat (1908-1940) in my humble opinion, so definitely check it out. Myriads of new words were created (some of them ex nihilo) in an attempt to modernize our mother tongue, & it was achieved without damaging the intelligibility of older texts too much.
Very nice and thorough clearing from 96314081311257. Just to add to the confusion "maga" also means "alone" (Maga maradt. = She/He was left alone.) or "self" (Maga készítette = She made it herself/He made it himself.).