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 humourlessness, which is a judgement 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 reported as far back as the Edo period, where it circulated among performers backstage, and there is documentary support for that period of use.

Which means the word went out of general circulation and came back. It resurfaced through television in the late 1970s and was carried into wide popular use in the early 1980s when it appeared in a hit song, after which it settled among young speakers and stayed.

Why the revival route matters

Because it is the ordinary way slang spreads now and it leaves a traceable record. A word appears in a drama, a musician uses it, and a generation adopts it. That path is documented in a way that Edo backstage speech is not, which is why the modern half of this word's history is much better attested than the older half.

It is worth being clear about that asymmetry rather than presenting the whole story at equal confidence.

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.