The idea is that you can initiate shaking hands with another player, hug another player, cuddle with another player or kiss with another player.
How it works:
You select it like you would select dancing and your view changes to third person similarly like when you dance. Your stance changes into putting your hand out, opening your arms or putting your head forward with your eyes slightly closed. When another player is then in close proximity he or she sees a prompt like how you can take a banana when one is offered. If another player accepts then you get both locked into an animation in which you shake hands, hug, cuddle or kiss for a short amount of time. If your offer for such an interaction isn't accepted your character shows slight disappointment through some funny animation and perhaps shrugs shoulders or performs an eye roll.
Important:
When you are both locked into the interaction you both cannot move and are vulnerable until the interaction has finished.
Reasoning:
When you play solo you can use this to express surrender of trust towards another bigger crew, or just show off that you are very brave, crazy or have nothing to loose. Because if you shake hands with the captain then the other crew members can kill you during the handshake.
When you are with a crew of two and are near a solo player you could also give each other a hug as a form of taunting. "We are so not impressed by you, that we even dare to go into this vulnerable state while you approach.", or it could be to show the other players that you don't have any violent intentions (at the moment at least).
Right now you can choose to be threatening to other players in your appearance, show it by drawing your sword. You threaten them with the unethical act of killing them. When you offer a kiss or cuddling then seduction comes into play. It can be an expression of affection and friendship like dancing or drinking grog, but it can also be used to distract someone while other crew members do something mischievous (like suddenly appearing and killing the person you're kissing with). "I am all alone on this island and just want a hug..."
It would also be nice to hug crew members as celebration when you completed a dangerous voyage.
Or imagine being on your sloop with your loved one after you just found treasure. The sun sets as you sail to the outpost. Then nothing is more romantic then kissing each other. (And nothing is more funny then when another ship or the kraken appears at precisely that moment.)
What I absolutely love about of Sea of Thieves is that there is complete freedom to be friendly or not. Whatever someone chooses is special, in the sense that it is not just always chosen because it is the most logical thing to do in the game. (I tried to be a pacifist in Halo Slayer matches for laughs. There wasn't a lot to do then besides getting killed.) This adds another option to be friendly, and because of the mechanic that both players get locked into a vulnerable situation for a short amount of time also opportunities to not be friendly.
And of course also just for laughs! grabs speaking trumpet: "Kisses for bananas".

