When you reach Big Buddy rank with your chosen Pokémon Buddy in Pokémon GO, you have the chance to receive gifts from them. Make sure you have the second heart under their name when checking out their buddy profile before trying to search for freebies.
Your buddy will find these gifts randomly as you explore the world. To make sure they have a chance to find them, you need to make sure their stomach is full in the lower left corner of your screen. If it's empty, you won't see them flying around your trainer avatar and you'll have to give them berries.
You will see a small gift wrapped under their buddy avatar on the buddy profile page. To receive the gift, you must "play" with them in AR mode.
When you first reach Big Buddy status, your Pokemon should have one immediately available for you to unbox. The items inside these gifts vary between useful berries and potions or even revive.
Many editors believe that you can only receive one gift from your friend per day, much like another friend can only send you one per day. If you have multiple Pokémon with Great Buddy rank or higher, you might receive many gifts because you can receive 20 gifts per day from all your friends. The system may operate similarly, but this is unconfirmed.
There are ways to quickly increase your buddy's rank, like making him excited or giving him a Poffin. You will have to spend time with your boyfriend and strengthen your relationship with him.