Synchronize is a rare ability in the Pokemon games. This ability will make an encountered wild Pokemon to have the same nature as your Pokemon who possesses the ability. However, there is only a 50/50 chance for this to happen in battle.
This also affects legendary Pokemon, it is a useful method when trying to obtain them with the nature that you desire. Also, if the Pokemon with Synchronize is at the end of your party list, the ability will still take effect at the start of the battle.
The nature mechanic in Pokemon is essential to IV Training; a complicated process that pros and veterans of the series are using in order to have stronger Pokemon.
Pokemon with Synchronize
A Pokemon with this ability that you can easily find in the game is Abra. The Pokemon is in the tall grass near Hau’oli City. However, it also has the Teleport ability which lets it run away in battle immediately. It is recommended for you to use a Fast Ball to catch Abra or you can just catch it as fast as possible with a regular Pokeball.