Your companions in Scarlet Nexus are extremely important, giving you more powers to access, and help in the fights you will encounter. To improve their abilities in combat you can increase their Bond Level, and one of the ways to do this is by giving them gifts.
Each characters will different gifts that they will prefer, and you can figure out what they are by speaking with the characters and listening to what they have to say over the course of the campaign.
To give gifts, players must first reach a specific part of the story called Standby Phase 2. This will be clearly marked in the story section of the main menu. Once you have reached the Standby Phase 2 section of the campaign, the ability to give gifts will unlock, and you can do so by interacting with any character. You will see a new option in their interaction menu to give them a gift.
Gifts can be found in the shop, where you can purchase them, or you can earn them by completing quests and side quests in the game. The final source for gifts is as floating objects when you are playing through missions. Be sure you track down and collect every floating object in the various missions to ensure you don’t miss anything important.