A popular hairstyle in the African-American community especially in the 1980's. This haircut was, as the previous entry says, a perm that loosens up the naturally tightened curls and makes the hair nice and bouncy as a result. The major downside to this hairdo was the extreme amount of maintenance it required to keep it looking pretty. Tons of hair care products made for a lot of greasy situations (no pun intended). Many jokes were actually aimed at this downside, see Coming To America (1988 film starring Eddie Murphy).
When Ricky got up off the leather sofa, his Jheri Curl left a greasy, oily stain where his head used to be. Guess how long that mess took to clean up.