She probably meant, "I'm dying to know." So she really, really, really wanted to know!

It is a very exaggerated slang phrase, but don't worry nobody is really dying. Her friend is only "dying of curiosity" because she is so super excited to find out about how the date went the guy. So it means she is "dying to know" about the details.

It means that her best friend, can't wait anymore, as in impatient ^^

Thanks all for your replies :-)

Dying can also be used to mean suffering badly: "Im dying with the flu" "im dying... I drank too much yesterday"