The extra, stretchy skin located on the elbows of thin or formerly overweight people. When the arm is straightened and the elbow skin pulled away from the arm, the dangling, flappy skin resembles the lips of the vagina (the labia). Hence the term, elbia.
"Damn!" Bones said aloud. "I can get drunk and play with my own elbia all night!"
"Oh, God! I think I'm going to be sick!" replied Mel.