It likely means “mourning girls” is being used to refer to girls who are grieving or showing sadness after someone has died, and “normal” suggests the speaker is asking what that looks like in everyday behavior.

Plain meaning

  • Mourning means expressing grief after a death.
  • So “mourning girls do normal” is probably broken or slangy wording for: “What do mourning girls normally do?”.
  • In normal use, that would mean things like crying, attending a funeral, wearing dark clothes, staying quiet, or following family traditions of grief.

Most likely interpretation

If this came from a post or comment, it may simply be a typo or awkward phrasing. A more natural version would be:

  • “What do mourning girls normally do?”
  • “What does mourning mean?”
  • “What do girls do when they are mourning?”

Simple answer

A mourning girl is just a girl who is grieving, and what she “normally does” depends on her culture, family, and the situation, but it usually involves showing sadness and remembering the person who died.

TL;DR

It means a girl who is grieving, and “normal” here is asking about typical mourning behavior, not something unusual or hidden.