"Honky Tonk Amnesia" is both a song, and a concept introduced by country icon Moe Bandy in this very tune. I'm not a big country expert, but I know that, like many country tunes, "Honky Tonk Amnesia" can be categorized as a "cheatin' song." The unnamed hero (or anti-hero) in the story wakes up after another night out at the honky tonk and slowly realizes what he has done. But the titular amnesia doesn't concern his not-being-able-to-remember the events of last night - quite on the contrary.
Indeed, honky tonk amnesia may best be described as a state of temporary insanity our hero regularly is subjected to once exposed to a significant amount of drinks at the local honky tonk: He forgets that he has a wife at home that he loves, and this forgetting makes him "look for someone else to love." Each time, he deals with the inavoidable consequences of this amnesia by lying to his woman at home about having to put in overtime, and as a trusting wife she believes him. The story remains unresolved by the end of the song, and it is more or less implied that the same thing goes on and on.
On a meta-level, the song's title might be interpreted as a comment on Bandy's own music and honky tonk music in general: Note that cheatin' songs have long been so common in country music that songs about cheatin' songs have become common, too. Each time Bandy writes a new song, he seems to forget that the previous one was also a cheatin' song, and that cheatin' is actually not a very good or positive thing, but because cheatin' songs are at the heart of honky tonk, he writes another cheatin' song.
Bandy's awareness of this conundrum is somewhat hinted at in the title of the album "Honky Tonk Amnesia" can be found on, I Just Started Hatin' Cheatin' Songs Today. In the title track, a man finds out he has been cheated on. Alone at the honky tonk, he suddenly realizes that he hates those cheatin' songs played there - presumably not just because they remind him that his wife cheated on him, but also because it were those same songs that soundtracked her cheating on him.