Moaning Myrtle is one of Hogwarts' many ghostly residents. She tends to float around in the castle's bathrooms (she died in one as a student) and chat with the students when they go in there.
She doesn't play a huge role in this particular story, but she's hanging around the prefects' bathroom when Harry goes there to try to decipher his clue for the next Triwizard task.
The scene is actually pretty bawdy and off color, thanks to the Myrtle's apparent (intense) interest in staring at young boys when they bathe. She gleefully tells Harry about how, by the time Cedric worked out the clue in the same bathtub, "Almost all the bubbles were gone!"
Oh, and she does say one other interesting thing in that scene that ends up being significant: she tells Harry she thinks she saw some Polyjuice Potion in one of the drains. Polyjuice Potion is used to change your appearance, and so if someone is using it, that probably means someone in Hogwarts isn't who they seem to be…which is good to know.
Harry doesn't really seem to pick up on the clue, unfortunately.