SM: Stands for "sadism/masochism" but is frequently used as a very general term for any kind of kinky or fetishy activity. "S and M" is dated--just say "SM."
BD: Stands for "bondage/discipline," but again, is frequently used as a general term. (The two terms are sometimes combined as "BDSM.")
D/s: Dominance and submission. D/s also stands for dominant/submissive, as in "Mistress Matisse is a dominant, and that person is her submissive."
top or bottom: This the most generic way of indicating people's roles.
switch: Someone who has the capacity to both top and bottom, not necessarily in the same scene.
sadist or masochist: Someone whose primary interest in SM is (respectively) giving or receiving intense sensation--e.g., pain. Being dominant and being sadistic are not the same thing, although one can be both. Ditto submissive and masochistic.
scene: A period of time during which one is doing actual SM activities. "They are doing a scene together." "Scene" can also be used to denote the leather/SM community as a whole, as in, "Is X in the scene?"
safe words: Words agreed upon by the participants that will modify or end SM play.
play: Used in the appropriate context, it means to do SM.
play party: A party at which people gather together primarily to do SM.
play-partner: Generally refers to anyone with whom one has BDSM encounters, but more specifically implies a casual, for-kinky-sex-only friendship and not a committed romantic relationship.
after-care: Time spent at the end of a scene to "come down," as it were, and gradually transition back to one's everyday role. Can be 15 minutes or several hours, depending on the people and the scene.