From Bulbapedia, the community-driven Pokémon encyclopedia.
Link is a measurement of the strength of the bond between a Pokémon and it's commanding Warrior or Warlord in Pokémon Conquest.
Developing a Link
A Warrior or Warlord links with a wild Pokémon using the link command in battle. When used, glowing orbs of light flash by the screen, and the player must press the A button as they pass by a cursor. This slowly charges up a link meter below the cursor, and when filled, the wild Pokémon is linked to and will be the Warrior or Warlord's to command after the battle is won. If the meter is not filled, it will retain its charge when another Warrior or Warlord tries to link with that same Pokémon, allowing several Warriors or Warlords to assist in creating a link. If a battle is lost or the player flees, linked Pokémon flee as well.
The potential strength of the link is represented by a coin icon over the wild Pokémon's head - a copper coin means a weak link, silver is moderate, and gold is strong. A coin crossed out means the currently selected Warrior or Warlord cannot link with the Pokémon at all. Pokémon owned by rival Warriors or Warlords also cannot be linked to. A Warrior or Warlord can link with as many Pokémon as their capacity allows, and can switch between them out of battle any time, developing links with each of them independently.
The base link level of a Pokémon varies depending on the Pokémon and the specialty type of the Warrior or Warlord. All actions taken by the Warrior or Warlord will develop the link further, and delegating a kingdom to train the Warriors and Warlords there will slowly increase the link. The fastest way to develop a link is through battling, even if the battle is lost, the link will develop. As the link grows stronger, the Pokémon's stats will increase, and periodically it's Range may increase.
Each Pokémon's Link with its Warrior or Warlord is displayed at the top of the screen in the Info window. The left percentage is the current link, the right percentage is the maximum possible link. Some Warriors and Warlords can only forge weak links with certain Pokémon, depending on their type specialty. A Warrior with a type specialty of Fire and Steel will link better with Fire and Steel-type Pokémon than Pokémon of other types. When a Pokémon's link with its Warrior or Warlord reaches its maximum value, it will gain no further link experience and its stats will not increase any further.
Each Warrior and Warlord has a Perfect Link, usually one Pokémon and it's evolutions. This Pokémon is the only one with which the Warrior or Warlord can develop a 100% link, taking the Pokémon to its highest possible strength. Though most Warriors and Warlords have only one Perfect Link, many Pokémon can form Perfect Links with multiple Warriors and Warlords. If a Warrior or Warlord links with a Pokémon that is their Perfect Link, they will state after the fight that they feel a stronger connection to the Pokémon than with other Pokémon they've handled.
Some Warlords need to transform and gain power in order to be able to maintain a Perfect Link if their partner Pokémon has evolved. For example, Nene has a Perfect Link with Golbat, but she must transform to have a Perfect Link with Crobat.
Evolution and Transformation
Link plays a crucial part in Pokémon evolution. Most Pokémon only evolve when a particular stat reaches a certain level, thus requiring a certain link level. Other Pokémon specifically need a minimum link level in order to evolve.
Warlords need a certain link level with a particular Pokémon to transform, such as Nene needing a link level of at least 70% with a Golbat to transform.
A Warrior or Warlord's link level with their Pokémon is reset when the player begins a new storyline, but the Warrior or Warlord will retain all Pokémon they linked to in previous storylines, in their same state of Pokémon evolution. If a Warrior or Warlord is dismissed from service, they will retain all Pokémon they linked to including their link levels.