Friendship points are the unit used in measuring an NPC's affinity toward you. Every NPC has FP (Friendship Points) as apposed to Love Points, which only exist in the thirteen Maidens. You can view an NPC's FP and LP in the relations menu by pressing + and scrolling to the right.
FP can be raised by speaking with the character whose FP you wish to raise every day. In addition, giving them gifts of their liked and loved items will increase their LP and FP much faster than just speaking to them every day.All characters, with the exception of the Iris sisters, can only be given one gift per day to raise their LP. If you continue to give them gifts, only their FP will increase. This works for all the characters in the game. For example if you gife Cinnamon about 20 fishes, her FP will increase by approx. 2 points, but her LP will only get 3-sub points. If you gife a Maiden a loved gift and after that a liked gift, her LP will get both 9- and 3-sub points. For example give Lara a chocolate cake and after that a strawberry.
For a detailed description on each character's liked and loved gifts, please visit their character page via the character portal.
As you earn more friendship points, new dialogue and events will become available. For instance, once Stella's FP are high enough, she will ask you to collect some scriptures from Selphy. Once unlocked, any given conversation will remain available forever, with the exception of conversations that are only available during and between certain events (such as when it is time to go rescue Mist and everyone is just randomly giving you luck). Also certain dialogue is only availabe on holidays.
Personal information is usually given at certain friendship levels as well. A character will usually say his/her birthday when at 4 friendship. The most hated items will be told 3 friendship, and most favourites are revealed at 4 friendship. Once you have 3 FP you may knock on an NPC's door by shaking the nunchuck in front of it.