This is a way to tell people (when they're using third person singular) to refer to you using singular they instead of he, she, or any other third person pronoun. Often (but not always), this means the person doesn't identify as a man or woman but is instead non-binary; you should use other gender neutral language accordingly, such as person.
There are other ways to verbally indicate this. It's probably most common to only give two forms with no separation ("they them"). This corresponds to how it's written ("they/them", with the slash not being pronounced). See my answer to Why do people use all 3 components in their gender pronouns?