The Buddy system is a new feature as of Version 1.7/0.37 where you can select a Pokémon that essentially walks with you. The Pokémon is tracked the same way as Eggs are. You can select your partner Pokémon and it will appear with you in the status screen. Depending on the size, it will either be behind your player, next to it, or even on the player's shoulder.

Shoulder	Behind	Side	Flying	Holding

Note: All Pokémon have just one position, except Pikachu. When you walk with a Pikachu, it will start off by your side, but when you hit 10km, it will move to the shoulder

There are sometimes special events that will halve the distance required for each Pokémon. In addition to this, Eevee's evolution into Espeon and Umbreon is contingent on Buddy distance. Reach 10km with Eevee as your buddy and evolve it while it's still your buddy for it to be Espeon in Day or Umbreon at night.

As you walk with the Pokémon, when certain distance milestones are hit, your Pokémon will pick up a Candy that matches its species line. This can be repeated multiple times so you can more easily collect candy of the Pokémon that you may not be able to find easily, allowing for Power Ups and Evolutions