What does ヤバい Yabai mean?

Yabai means dangerous, and it also means excellent. Both senses are current, the older one is the negative, and speakers rely on tone and situation to sort them out.

Where it started

The word began as criminal slang, first cited in an 1892 cant dictionary, meaning that a situation had become risky: a warning that the police were getting close. An older form, yaba, meaning illegal or dangerous, appears in sources from the late 1700s. The negative sense held for a long time and is still perfectly usable.

The reversal

Younger speakers began applying it to things that were overwhelming in a good way. A meal, a performance, a piece of animation. The sense is not that the thing is dangerous but that it exceeds normal description, and the older negative meaning did not disappear to make room.

English has done this repeatedly. Bad meant bad and then also meant excellent. Sick, wicked and insane all took the same route, and in every case the intensity survived the reversal while the polarity flipped.

Why this is not confusing in practice

Because the word does not carry the polarity; the delivery does. A flat, urgent yabai on seeing a bill is not the same utterance as a drawn-out one on tasting something.

This is exactly what English does with no way. The words are identical and the meaning is entirely in the performance, which is a thing languages do routinely and dictionaries record badly.

The subtitling problem

A subtitler has to pick, and picks differently every time the word appears, so a viewer watching with subtitles sees one Japanese word rendered a dozen ways across a series. That looks like sloppiness and is the opposite: each rendering is choosing an English word for the specific intensity in the delivery, because English has no single term that spans both poles.

The register, which is the part to keep

Casual, young-leaning, and not suitable for formal situations in either sense. It is a word for friends, and using it in a work meeting reads roughly as an English speaker saying something is insane in a board report.