Taffey Lewis is the owner of Taffey's Snake Pit Bar in the Fourth Sector where much entertainment occurs. There is music, exotic dancing, something being smoked in pipes. But the place isn't downmarket - all the clientele seem to be well dressed. Taffey is obviously used to policemen and has little time for them. Deckard's threats don't wash with him and he dismisses Deckard with a free drink.
Deckard invites Rachael to join him, but she says it's not her kind of place. Deckard then sees Zhora and waits for her backstage, before gaining access to her (shared) dressing room through a quickly thought-up deception. After she discovers Deckard's intentions, she punches Deckard, and escapes. After a chase through Los Angeles, Deckard shoots her three times, killing her.
Leon turns up (presumably to meet his "girlfriend" after she finished her performance). Luckily for Deckard, Rachael decides to come down to see him after all, and she finds Leon attacking Deckard. Rachael shoots Leon in the head and kills him.
Taffey was played by Hy Pyke. An interesting bit of trivia is that although Ridley Scott is a notorious perfectionist when it comes to shooting and reshooting scenes, Hy Pyke managed to play Taffey perfectly in one take.