"Izakaya" literally means "sit-down-saké-shop".
Saké dealers in the Edo era set up tables and benches in their shops to serve inexpensive saké by the cup (actually a masu, a small wooden box used to measure rice). Eventually various kinds of sakana (food that goes well with saké) were served as well.
Most izakaya function more or less as clubs in that they have distinct styles and a regular clientele. The patrons assume a seating order based on their seniority as long-standing or newer customers. While anyone is welcome to drop in, the regulars are nomitomodachi ("drinkin' buddies").
Often the mama-san who owns the izakaya will serve very particular kinds of saké.