I got a dog T-shirt from my friend and it says 'practically famous' on top. I don't get the meaning.

What is being practically famous?

Mary Poppins was "practically perfect." We use it to mean "nearly" - "nearly famous."

Probably the origin is something like, "for all practical purposes," or "for all useful purposes, " or "for all intents and puposes." ( This last one was very common in my day.)

The wheel may not be [perfectly] round, but it's practically round. In other words, for any purpose you intend, it's round enough.
I see. Then I think it would be better if the T-shrit have said 'perfectly famous' rather than 'practically famous.'. Thanks, Avangi.