Bond Phenomenon

The Bond Phenomenon (キズナ現象, Kizuna Genshou) is a where a Pokémon can bond with its trainer to activate an ability which is similar to Mega Evolution.

History
Not much known about this ability, but according to Professor Sycamore, it said that the phenomenon once occurred several hundred years ago and rarely happens when the mutual trust between trainer and its Pokémon is high and they master it. Sycamore also noted that the phenomenon was related to the Pokémon's potential ability and it doesn't happen to just any Pokémon.

Ash-Greninja
One example of the evolution is shown by Ash's Greninja. During the battle against Heidayu, Greninja's strong bond with Ash temporarily activates the Ash-Greninja phenomenon and allows them defeats Bisharp before reverting back to normal.

According to Clemont, when Ash and Greninja have exact same feeling, Greninja's appearace will take resemblance like Ash. Serena even recalls Olympia have told them that Greninja will receive full power which would prevail over greatness.

Abilities
Its full capabilities and attributes were initially unknown, but it appears to give a significant boost in speed and power. They also share each other's point of view. In his second form, he has a full form that surpasses even the strongest Mega Evolved Pokémon with the Water Fuma Shuriken on his back which can deal massive damage to, if not defeat the strongest of his opponents in one hit.

Ash-Greninja
Despite increasing Greninja's speed and power, it comes with the side-effect: If Greninja was attacked and takes damage, Ash will feel his pain as they shares each others pulse, so if it is pushed too hard, Ash may collapse from exhaustion. It was soon revealed that the main reason Ash & Greninja were having trouble with this form is due to Ash not having complete faith & trust with his Greninja.

Trivia

 * This type of evolution does not appear in any of the games, as it was made exclusively for the anime.