Red Kryptonite is a varietal of Kryptonite. It has various effects on Kryptonians. In the Silver Age comics and Lois & Clark: The New Adventures of Superman, it has a different effect each exposure to the Kryptonian; in Smallville, it removes their inhibitions.
An artificially made Red Kryptonite was created by Batman using Green Kryptonite and radiation experiments before the JLA Tower of Babel story arc as a means to disable Superman if he ever went rogue, but it was stolen by Ra's al Ghul for a more lethal use. Exposure to the artificial Red Kryptonite made Superman's skin become transparent and caused him to feel intense pain as well as overload his natural solar absorption to the point his super senses were overwhelmed.
Another artificially made Red Kryptonite was created by Mr. Mxyzptlk and given to Lex Luthor as a gift. This chunk of Red Kryptonite acted similar to Gold Kryptonite, in that it robbed Superman of all his powers. The only way the process could be undone was a rule Mxy put in place for Lex: Not to reveal that he was behind the creation of Kryptonite. If Lex revealed he made it, its effects on Superman would cease.