This article seems to provide good information on the ritual. Excerpts:
Henna use, both for everyday adornment and for ritual purposes,
quickly spread throughout the Diaspora and was an established custom
among the Jews of Morocco and other North African communities, the
Levant and Mediterranean basin, the Arabian Peninsula, and Western,
Central and Southern Asia.
In these communities, henna was a crucial aspect of the preparations
for a Jewish wedding, and often defined the structure of the wedding
festivities, from the beginning (marked by the sending of henna from
the groom to the bride) through the climax (the main henna ceremony
itself) to the end (when the last remnants of henna wore off the
skin). Furthermore, henna was used to mark the actors in a variety of
other lifecycle events and passage rituals, such as birth, weaning,
entering the school system, puberty, and coming out of mourning. It
was also used at holiday celebrations and other happy occasions. The
symbolism of henna in these Jewish communities was highly polysemous,
but it is clear that it had three overarching functions: first, the
henna’s staining of skin was seen as beautifying, both as daily
adornment and for weddings; second, the materiality of henna was
thought as protective, especially of actors at the center of a passage
ritual; third, henna was seen as an aid in transforming and guiding
the actors into the structure of their new social roles.
One of my friend's daughters had a henna ceremony last year. Unfortunately, because I was in mourning, then, I couldn't attend, but I would have been curious to see what this was. I guess there must be some video on YouTube or some other web site.