The claws can also be used to scale buildings and cut class cases during heists.
In her first costume made in the apparent she shared with Holly Robinson, claws were on Selina's gloves. The media was discrediting Batman for her early endeavors. To establish herself on the scene she began using her claws to "mark" her enemies starting with her pimp, Stan. She also left permanent scarring on Carmine Falcone's cheek.
Later as her wealth grew she constructed stronger retraceable claws on her gloves and boots to scale buildings.
In combat her claws have been shown to be strong enough to damage Cyber Cat's power armor.
Background Information and Notes
Originally Selina scratched people with her actual fingernails in The Batman vs. the Cat-Woman written by Bill Finger in Batman #3 (September 1940). By the The Princess of Plunder story in Batman #10 (April 1942) she was wearing clawed gloves. They have since become a staple of Catwoman's character, appearing in nearly every major Batman television and movie adaptation to date. In the revamped origin in Batman: Year One she has only claws starting out, not yet taken up use of a bullwhip.
Usage in outside media adaptations
The claws in Batman Returns are shown to be made from found objects in Selina's sewing nook. They are employed in physical confrontations throughout the film, in one scene they penetrate at weak spot in Batman's armor. At the end of the film she sticks the claws into a cable on the Penguin's generator to kill Max Shreck with her stun gun, seemingly using her own body to channel a powerful electrical current.