To drink oneself unconscious or to get so drunk that one becomes incapacitated/passes out; a colloquial expression.
昨夜は飲みすぎて駅前で酔いつぶれてしまった。
I drank too much last night and passed out in front of the station.
彼は毎週末バーで酔いつぶれるまで飲む。
He drinks at the bar every weekend until he passes out drunk.
友達が酔いつぶれたので、寝袋に入れて休ませた。
A friend passed out drunk, so I put him in a sleeping bag to rest.