Perks are a feature introduced in The Elder Scrolls V: Skyrim.Every time a level is gained, a point is granted to spend on a perk. However, points don't need to be used immediately; they can be saved for use later if you don't have the Skill level you require to have the perk.
Each perk will have certain requirements before it can be chosen - for instance, perks after Shield Wall require a Block level of 20, and higher-level perks, such as Shield Charge, require a Block level of 100.
Skill prerequisites aside, most perks for a given skill depend upon a previously obtained perk. The exception being the starting perk, that must be obtained first in order to obtain any other perks for that skill. The skills of destruction, restoration, alteration, heavy armour, sneak, lockpicking, pickpocket, and speech all have a perk dependency structure that is a rooted tree. Hence the term, perk tree.
Other skills do not have perk trees as they contain multiple paths converging on the same perk; trees do not grow in this way. Nevertheless the term is sometimes still used.
Some perks in a tree cannot be obtained by looping around another path, after reaching the end of the tree. An example of this is on the Smithing tree. The Daedric Smithing perk, which comes before the Dragon Armor perk, cannot be obtained from the left side of the tree, despite the Dragon Armor perk being visibly joined to the Glass Armor perk.
Perks are detailed on the individual skill pages, along with their requirements.
There are 251 perks in the game. Originally, there was a level cap of 81, which meant a maximum of 80 perks were available. As of patch 1.9, this limit has been lifted with the addition of Legendary Skills. This addition grants the ability to level up past 81 by resetting skills trees back to level 15 (giving back any perks spent in that tree), thus gaining more perks.
With the addition of The Elder Scrolls V: Dragonborn, completing the main questline grants the option to reset all the perks in a skill tree at the cost of one Dragon Soul. The perks are returned and can be spent elsewhere.
This is useful for perks that are not always active, such as Smithing and Enchanting, as the Dragonborn can move the perks for other skills when they are not in use.