Nobody knows that. It's possible it's because of the Miracle Elixer. It's also possible it's because she's a child of both worlds. Nobody really knows though. They don't say in the musical.
In class when Dr. Dillamond gets taken away and Fiyero realizes that elphie is really good and when they are saving the cub... and it just kinda happens! :)
Why did elphie ask glinda to come with her to the emerald city?