Friendship is how the players relationship with Characters is measured.
Completing quests, doing activities that expend energy while hanging out, having daily discussions, serving meals in Chez Remy, or giving characters gifts will increase Friendship level.
Friendship levels for each character can be leveled up to 10, and each level awards a prize - many of which are unique items.
Tip: When trying to level up the characters, go into the Menu>Collections>Characters. There will be a list of all characters there. If you put your cursor over a character, in the bottom right-hand corner will be a list of their three "favorite things of the day". Giving one or more of these items to the character will produce extra friendship stars so they will level up faster! (The items can consist of anything that comes from anywhere in the game, so it is possible that a character's current favorite item(s) of the day may be something(s) you do not have access to/cannot make yet.)