Following Pokemon was first introduced back in Pokemon Yellow and was again seen back in Pokemon HeartGold & SoulSilver, and this same concept returns in this very game. On top of your Starter Partner Pokemon always being with your trainer, players will also be able to select another Pokemon to follow them outside of their Poke Ball (done through the Party Menu). Except for the handful of Pokemon that players will actually Ride on when they are outside of their Poke Ball, every other Pokemon can follow your trainer whenever you would like them to, including Legendary Pokemon. (When two players are playing the game, both can select a Pokemon to follow them.)
When traveling alongside your trainer, following Pokemon will often stop to check out various things in the world depending on their given Pokemon Species. Some Pokemon will even find certain hidden Items found in both bushes and caves during your journey, which you can then obtain by interacting with them. While out of their Poke Ball, these Pokemon will gain more affection towards your trainer. The higher a Pokemon's Affection Stat is, the more likely they are to land Critical Hits in battle, avoid attacks in battle, survive certain attacks in battle with one Hit Point, and naturally remove status conditions they obtain when in battle.