Fish are a type of monster that appear on the 22nd and other Floors' lakes and can only be found by fishing.
In order to catch a fish, a player needs to meet the prerequisite in fishing skill, which differs for each fish and lake. The lake near Kirito and Asuna's log house contains the "local-god" fish, making it the most difficult lake for fishing.
Chronology
Aincrad Arc
After getting married and moving to the 22nd Floor with Asuna, Kirito wants to fish at a local lake. But little does he know that the lake he picks to fish in has a monster, the local god fish which greatly increased the difficulty in fishing in the lake, so he was not able to catch any fish. Later, an old man, an experienced fisherman, helps him out. With that, Kirito helps fish out and defeat the monster of the area.