What does it mean when you have no room to talk?

It means the same thing as if you were to replace "you have no room to talk" with "you are in no better position to comment on the subject,"

Because you are in the same position as the other person; or have the same faults; or have comitted the same act as the other person, it is often seen as morally unjust to place blame on them.

If another person has mud on thier pants and they are making fun of you because you have mud on your pants, they have no room to talk.

If you cheated on your boyfriend and are getting mad at him for checking out other girls, you have no room to talk.