Fishing is a skill that adds a whole new aspect to fishing and a much more useful and productive task. Fishing has a chance of finding useful loot and abilities to get catches more often. There is also the shake ability, which allows you to retrieve mob drops from mobs without having to kill them.

Here are the Abilities:

Treasure Hunter
Fish up misc. objects

Magic Hunter
Find enchanted items.
Magic Hunter is an ability that allows armor and tools obtained from Treasure Hunter to be enchanted, chances of which starting at 5% (rank 1/5) at level 1-199, and increasing by 5% per 200 Fishing levels. At level 800, the probability is 25%.

There is also a rain bonus. It increases with fishing level and the maximal bonus for Magic Hunter is 2.50%. As such, the maximum percent of Magic Hunter with rain bonus is 27.50% on 800 level of fishing. Some servers disable this skill, as it gives rare items, which can be farmed.

Ice Fishing
Allows you to fish in icy biomes.

Master Angler
Improves chance of getting a bite while fishing.
As of the 1.7 update, Master Angler is unlocked at level 125 and allows you to receive 2 different multipliers for your bite chance. By default your bite chance is 0.2% per tick. There are 20 ticks per second, but due to lag, ticks don't happen uniformly, and on laggier servers, one may have a harder time catching fish. You can multiply your bite chance by 2 by default by either being in a river or ocean biome, or being in a boat. These do stack, and your bite chance can go up to 0.8% because your bite chance was doubled twice. With rain, you can increase your bite chance even more.

Keep in mind that in this case, lag refers to the ticks per second, which is made obvious by the rate at which entities move. If you can break a block and it takes a while to pop off as an item after breaking it, it means the server's game loop, the ticks, was slow and this the block didn't update. Mobs also tend to move very slowly with constant lag, but lag spikes result in you not affecting anything and mobs suddenly fast forwarding to catch up for missed ticks. (Often resulting in death if outside and vulnerable)

Take Items off of mobs with a fishing pole
Shake is an ability that allows the player to get items from mobs by hooking them with a fishing rod. It can be used repeatedly for a large number of items depending on the remaining health of the mob. However this reduces the durability of the fishing rod drastically. The fishing rod, when used in this method, will always deal damage equivalent to 25% of the maximum health of the mob. Keep this in mind when fighting tougher creatures (such as Iron Golems), as a single shake will deal a considerable amount of damage. If fighting tiny magma cubes / slimes, a single shake will kill the mob. You also have a small chance of getting that item a monster had, for example an iron shovel or gold helmet.

Fisherman's Diet
Improves hunger restored from fished foods
This ability increases the number of hunger units regenerated by consuming fish. It is measured in ranks increasing once every 200 levels, each rank increasing hunger regeneration by one unit (a single unit being half of a piece of meat on the hunger bar).

I hope this has helped you!