Minecraft wiki entry for Fish_farming, associated text: Use an enchanted fishing rod, spending XP on a fishing rod may seem useless, but it is not, you can get amazing loot from fishing. There are 4 enchantments useful for fishing rods: Mending, Unbreaking, Lure, and Luck of the Sea. You can also catch enchanted fishing rods as "treasure" -- they will be fairly damaged, but as soon as you find one with Mending, you can use that (it will heal itself as you fish), and combine other rods with it as you collect the various enchantments. Eventually you will end up with a "god rod": Mending, Unbreaking III, Luck of The Sea III, Lure III. Even if the last couple of anvil combinations are expensive, it's worthwhile, because once you have the full set of enchantments, you'll never need to use the anvil on that rod again.
Mending + Unbreaking
Mending can be useful because you get enough XP from fishing to keep the rod at full durability with just Mending. Unbreaking simply stops the rod from breaking as fast, so it will require less mending and leave more experience for you.
Luck Of The Sea
Simple, it gets you more treasure and less junk.
Lure
Lure decreases the pre-determined wait time (5-30 seconds) by 5 seconds with each level (minimum 0). With Lure III, catches will be immediate half the time, and up to 15 seconds the rest of the time.