No me trate de usted

No me trate de usted
 

¿Cuál significa esto?

I think you more commonly you would hear
no me trates de Ud.

This means please use tú when you address me. (or in your case vos)

"Qué" because you are asking for a definition or description.

Depending on context, I would interpret this as one of the following:
1. an invitation to use familiar address (tú/vos) instead of formal address (usted). I would expect "no me trates de usted".
2. an invitation to be less formal.

which is the informal form. So if someone said "no me trate de usted", does that imply that they want the other person to speak informally to them, but that they will continue to speak formally to the other person? Or that both of them will start using the informal form?

[quoted message edited as an answer]
That one.

Otherwise, they'd say "no nos tratemos de usted".