She's a symbiotic species with a slug-like creature in her. The humanoid part only lives about as long as a human, but the slug lives for many centuries and when one host body dies, the slug is moved to another. It contains memories from previous hosts. This scene was from shortly after one host died and the slug was moved into a new one, who wasn't quite as prepared for the transition.

Ok, it was mentioned that she is a Trill with a symbiote that moves from host to host, BUT a couple relevant points.

1 - The worm (symbiote) that lives in them merges with the host, combining personalities. This symbiote has been joined to eight hosts at this point, which means there's about that meany people's lives in there.

2 - Not all trill get a symbiote, they typically go to a special academy and need to be in an elite group to get one. Once you merge, you can't unmerge without killing the host.

3 - this host, Ezri, was untrained and would not normally get a symbiote, but the previous host was killed and she was the closest available host, so she was assigned this symbiote without being properly prepared.

4 - two of the previous hosts - Curzon (a male host) and Jadzia (a female host) were extremely popular and well respected, which put a lot of extra pressure on the current host, leading to a lot of self doubt and personal identity confusion.

She's a Trill, a being that maintains its prior memories from host to host.

This is Ezri Dax.. She is a Trill. Some trill host symbiotes. The symbiotes live longer than their hosts. During hosting memories and personalities blend, and the symbiote will carry that blending into the next host.

Her symbiote is named Dax and was previously hosted by both another female, Jadzia, and a male Curzon, and several others.

Jazdia Dax was the name of Jadzia hosting Dax. Curzon Dax was the name of Curzon hosting Dax.

A long lived slug lookin thing that lives inside a humanoid host body and kinda merges their personality and memories. Ezri is like the 8th host to Dax.

If you're gonna hang out in a Star Trek fedicomm you're probably gonna wanna watch TOS (The Original Series), TNG (The Next Generation) and DS9 (Deep Space Nine) at a minimum. They're quite good, but fair warning: the special effects are pretty dated, especially in TOS. The writing and acting hold up terrifically, though.