By selecting a Pokémon as your buddy, you can build a relationship with them and gain special perks as your relationship deepens. As you interact with your buddy, you'll earn Affection hearts and improve your buddy's Mood, a measure of how happy your Buddy feels.

What does great Buddy do?

Great Buddy

May help you with catching Pokémon! When a Pokémon you're trying to catch hits a Poké Ball back at you during an Encounter, there's a chance your buddy will help you out by bouncing the Poké Ball back at the Pokémon. May pick up consumable items like Berries and Potions and deliver them to you as presents.

Do Buddy souvenirs do anything?

These souvenirs, according to Niantic, are essentially just reminders of your adventures with your buddy. That's it. You can view them from the buddy page, but they don't do anything but sit there. It's essentially just a marker of how long the Pokemon has been set as your buddy.