To party with no inhibitions; i.e. unleash the beast. The phrase was originally made popular by the worst song of all time, "who let the dogs out?", but now is used mockingly.
Since the world is supposedly going to endtomorrow, I am going to let the dogs out tonight.
Used in polite circles when you are out on the lash need to go home for a poo. Best used with embellishment.
Brad: Sorry lads but I have got to go home and let the dogs out.
Angelina: I thought so, they have been barking all afternoon.
Brad: Yeah, if I don't go now there will be horrible mess.