It's an expression that pirates say in fiction stories. In Standard English, it would be "shiver my timbers", but pirates replace "my" with "me", so they say "shiver me timbers". It's a way to express shock. If you want to know its literal meaning, "timbers" refers to the wood of the ship, and "shiver" refers to when the ship shakes when there are big waves, which shocks the pirates. It's not an expression that's used in real life. It's just an imaginary expression that's used when writing stories about pirates.

It means that the speaker is pretending to be a pirate. "Shiver me timbers" is just a thing that pirates say in books and movies. It has no real meaning beyond that.

Yay, A pirate saying! It's usually used in pirate literature, and expresses a feeling of shock or surprise. Literally, "timbers" refers to the wood that pirate ships were made out of, so "shiver me timbers" is like saying "shake my boat"... basically.

I agree it's an expression of shock, but I think some commenters have forgotten the other meaning of "to shiver", which is to split into splinters. The piece of wood is totally destroyed. That's a shock indeed!