What does マジ Maji mean?

Maji means seriously, in the sense of no joke, really, are you telling the truth. It is a shortening of 真面目 (majime), which means earnest or diligent and is a perfectly respectable word.

The parent word

真面目 describes a person who applies themselves and takes things seriously. It is a compliment, though a slightly double-edged one: a person can be so earnest that the word starts implying humorlessness, which is a judgment English makes about the word serious too.

The clipped slang form kept the truth-and-seriousness sense and discarded the character assessment entirely.

An older word than it sounds

It is not a recent coinage. The slang use is attested as far back as the Edo period, in a book of 1781, Nyan no koto da.

That 1781 example uses it as a noun, in a phrase about becoming maji, turning serious. Present-day use is mostly adverbial, with maji set directly before what it intensifies, as in maji bibitta, really scared. In sore maji de?, is that for real?, it is still a noun.

Other spellings and a rival

The kanji 本気 are sometimes borrowed to write it, as in the title of Ayumi Tachihara's manga Maji! (本気!). More recently gachi, clipped from gachinko, has come into use with the same meaning.

How it is used

Alone, as a challenge to something implausible. Attached to a following word, as an intensifier meaning genuinely or properly. In a common set phrase, as an expression of disbelief that has become almost automatic.

The register is casual and would be out of place in formal speech, where the unclipped parent word is entirely at home. The two forms have drifted far enough apart that using the long one as slang would sound like a joke.