Everyone has strings coming from their hearts that connect to other people. They are connections of love. Though it can be any kind of love; romantic, platonic, familial, etc.
The more you love someone/thing the thicker and more visible the bond is.
In the past people thought these bonds proved you had a soul, because how could someone have a soul if they didn't love a single person?
They snap due to the death of one of the individuals with the bond, if one side betrayal the other in a way that hurts them so deeply for at least one moment they can not feel a single ounce of love for the other, or it will gradually split apart and snap if the feelings fading away over time.
A snapped bond hangs like a cut thread from the chest for as long as the owner thinks about the other. If they move on the thread will eventually fade away from visibility.
The broken bond does leave a mark on your soul even if it has faded from view. The bonds branch our from the soul like strings from a yarn ball. So when they are cut they unravel a bit of the soul and leave a hole.
This hole cannot heal naturally even if the person moves on it can only be replaced, or over time the opening will be carefully patched over (if the owner truly moves on), but the hole on the inside will remain.
Broken bonds cause physical pain to the owner, so society places high importance on the bonds. Parents warn their children to be careful who they bond with because they have to be wary of broken bonds and the pain they cause, because eventually if you get to many holes your soul will unravel, and it kills you.
The cause of death due to having too many holes in a person's soul is called unraveling.
People don't care if you have less bonds but only if the ones you have are thicker to account for the lack of multiple bonds. It's uncommon for anyone to have less than three bonds. At least one really strong and two weaker ones. So people with less than three are judged heavily by society.
Those with many thick bonds are considered very loving and are looked on well by society.
Those with no bonds or broken bonds are considered soulless and are pariah, while those who only have broken bonds are looked at in pity or disgust because only those who have lost everything or are criminals should only have broken bonds.
Below is finally the Tobirama part of this post. ⬇️
Okay so now that I've spent an age explaining the bond concept here's the Tobirama part of the concept.
Tobirama as a child started off with the familial bonds like most children. He has six bonds: Butsuma, his Mom, Hashirama, Kawarama, Itama, and Touka.
He did not have thick bonds from the beginning with his father. It thinned, frayed, and snapped the first time he hit Kawarama or Itama.
He had a thick bond with his mother.
He had thick bonds with Kawarama and Itama. He would never admit to having a favorite but Itama's was slightly thicker.
He used to have a thick bond with Hashirama but since the river it started to fray over time before finally snapping the first time Hashirama told him he was nothing but a tool to end an argument.
Touka's grew thicker over time and by the time the clan war's are ending is his only remaining bond.
Tobirama never gained any platonic or friend based bonds because due to his coloring and attitude was isolated by his clan. Tobirama lost two agemate playmates this way. Parents driving them away from with frowns, grimaces, and whispers of demon. Leaving him with two holes in his soul.
Clansmen made a game of seeing if young Tobi would bond with them to break it on purpose. It started as an order from Butsuma to make him a better weapon then became a game. This occurred three times before he noticed the pattern and closed himself off because he now had another three holes in his soul.
Tobirama had gained five holes in his soul by the time Itama died at the hands of his clansmen and no longer trust them to make bonds. The breaking of his familial bonds except Touka leave him with ten holes in his heart.
For this AU ten is an extreme number and most people would have unraveled at this point, but Tobirama is stubborn and keeps going.
Tobirama gets two more from people he's gotten close to on missions he was unable to protect or save. With twelve holes in his soul Touka is heavily concerned for her 'brother', but he's sent out on another mission where he gets close to a child and develops a bond with them only for them to die, enemy-nin or illness you decide.
Tobirama knows after that last snap at unlucky number thirteen that he's going to unravel. He informs the elder council who give him one last suicide mission for him to die on and benefit the Senju one last time.
On that mission he encounters Kurama and impresses him. Kurama seeing the damage decides that finders keepers and if they can't take care of the pale kit then the kit is his now.
Tobirama gains a bond filling in the place of his father's bond.
Matatabi gets enlisted to go check on Kurama by the other bijuu since he hasn't been seen in ages, and is impressed by the kitten Kurama has adopted and decides to stay and help nurse the kitten back to help, because she doesn't trust Kurama to not kill the human kitten.
Tobirama gains a bond filling in the place of his mother's bond.
Overtime Tobirma befriends each of the bijuu and they fill in his bonds. Then the gods check on their children to see why they've congregated and see the human packed to the brim with thick familial bonds with their children. And decide what can they do but except his as family as well.
Here are the bond relations I imagine.
Grandmentor: Susanoo (Water god)
Grandmother: Ameratsu (Fire goddess)
Grandfather: Tsukuyomi (The *Actual* moon god)
Godfather: The Shinigami
Annoying Aunt/Uncle: Shukaku
Mentor: Isobu
Friend: Son Goku
Brothers x 3 to replace Hashirama, Kawarama, and Itama: Kokuo, Saiken, Gyuki
Excitable cousin: Chomei (wind chakra)
After getting bonds with all of the chakra beasts Tobirama becomes a pseudo Juubi. Closer to the wolf form we all headcannoned before learning about the god tree shenanigans.
While Tobirama is getting a new family, back in Senju and Uchiha land. When Tobirama was sent out on a suicide mission the council sent Touka out on a year long mission because they knew she'd become rabid if she found out what they did. Hashirama unable to run the compound as efficiently without Touka and Tobirama loses ground against the Uchiha. Supplies, contracts, and shinobi start dropping without the two their to manage it. Hashirama asks the council about their whereabouts and is told they are both on long term critical missions.
The good thing about the Senju loosing ground and numbers is the Uchiha gain it. So that the two clans are more on equal terms and relaxes the Uchiha into agreeing to a cease fire. The Uchiha have spies in court that have seen Touka so they know where she's been for a year, but no one has seen Tobirama so they assume he's dead.
Once they start planning the village Madara offers his condolences for the death of Hashirama's last brother, and oblivious sub!optimal Hashirama states Tobi's not dead and goes to grab his soul bond and notices it gone, pats around his chest frantically and doesn't find a snapped soul bond, only for Mito to tell him confused he doesn't know that his bond with Tobirama snapped over a year ago.
Hashirama is horrified, and finds out about the suicide mention and Tobirama's unraveling from the elders, and frantically goes searching for him.
Only to find a healthy, happy, choke full of soul bonds Tobirama surrounded by gods and monsters that are pissed about his prior treatment.
And this could all be shortened backstory for a very lovely Tobirama x (someone but we all know I prefer Madara or Indra).