To be out as a transgender person means to share both their sex and gender openly. An out transexual will share their gender at birth with others. Being out signals a high amount of comfort and confidence in themselves and sometimes a socio-political attitude that wants to fight the stigma of transgenderism.
The vast majority of trans people are not out. Some people may be out in only some parts of their life, such as family and friends, but not others, like strangers. Always assume a person is not out unless they have specifically said so. If in doubt, just ask!
Outing someone refers to revealing a trans person's gender at birth against their will. Outing may be intentional, wanting to humiliate the person, or accidental, like using the wrong pronoun. Outing someone else is never appropriate. Done on purpose, it says to the person, "I care more about telling everyone what I think than you looking like a fool."