It's a Mexicanism for rambling, "hanging off with something incoherent," even for "stun with psychotropics." As it is not incorporated into the official dictionary there is no true etymology, although there are already several attempts to find it an origin. The most obvious is the least believable, since French verbs such as débrayer (I debraié "disconnect, skate a clutch in a gear change") ), débrouiller (debruilé "unroll" ) or until débrailler (debreié "show the torso, in women is out of control mo mo ) have no documented contact with Mexican slang. So it becomes more believable a dissimilation with deranged metasis, eliminating the 's' , modifying 'var' with 'bra' and finally replacing 'i' with 'y'. It seems a lot, but let's imagine that it was oral transmission and poorly pronounced from the beginning, so it already makes a little more sense. See debraye.
Debraye is also used in the sense of having a conversation or a monologue that changes the subject of erratic or seemingly erratic. You wander, but it is not necessarily to say things without meaning or stupid, its characteristic is the thematic freedom. In a debraye we can be talking about a trip to Florence, mentioning the Church of Santa María de Fiore, there pass to Miguel Angel Buonarrotti, and mentioning his homosexuality, finish talking about homophobia and discrimination in general.
