BTR stands for "back to room." This term is used to explain a hook up (typically of the drunk college type) that begins in public and progresses to one of the participant's dorm/frat bedrooms. Typically, sexual acts more serious than kissing/making out occur when a couple enters a bedroom, so this term implies a more intense encounter than the simple "make out in public."
Origin: The Claremont Colleges, circa 2008. Large five college dance parties foster an atmosphere where both men and women will kiss/make out with multiple partners at a single dance party. Many of temporary couplings are not serious, but are still considered "hooking up." The term "back to room" entered conversation to describe the scenario when a couple actually left the dance party together to continue hooking up in a dorm room. Through very frequent use, it has simply become the acronym BTR.
BTR is most commonly used as a verb (see below).
Student 1: Yo! I heard you hooked up with _____ last night!
Student 2: Haha, yeah... We just made out on the dance floor (DFM) a bit, whatever.
Student 2: Yeah... We BTR'd and we're up until 4am.
Alternate Use: Yeah... We went BTR and we're up until 4am.