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 for every exposure to Kryptonians; in Smallville, it removes their inhibitions.
An artificial red Kryptonite was created by Batman using green Kryptonite and radiation experiments as a means to disable Superman if he ever turned evil. Exposure to the red Kryptonite made Superman's skin transparent and caused him intense pain as well as overloading his natural solar absorption to the point where his super senses were overwhelmed.
Another artificially made red Kryptonite was created by Mister Mxyzptlk and given to Lex Luthor. This chunk of red Kryptonite acted similar to gold Kryptonite, as it removed Superman of 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, the effects on Superman would end.