"GIve" here means to give way, break, collapse. It means something is going to break or collapse under intolerable pressure. It can't stay that way forever: sooner or later "something's gotta give." It could be a structure that is going to break under too heavy a load, or it could refer to two opposing forces, temporarily balanced, one of which it about to give way to the other. The phrase became very popular when it became the title of a song by Johnny Mercer in 1954, where it refers to a romantic encounter or "battle of the sexes:" "When an irresistible force--such as you, Meets an old immovable object like me, You can bet just as sure as you live-- Something's gotta give! Something's gotta give! Something's gotta give!" The song can be heard hear, beginning at about 1:19. Notice that he actually sings it as "Somep'ns gotta give!"

This refers to a "give and take" relationship between people. When two people are at a conflict and neither wants to budge, the only way to resolve the conflict would be for one of them to "give", meaning that they surrender something to the other side or compromise. In other words, mean that there is tension in something, like a conflict, and in order to resolve the conflict, someone has to break the tension and cause it to "give way" (yield to something or someone).

Kira commented: "After your explanation I can also understand this phrase as 'something is about to change', am I correct?" My answer to this is: Probably, but it always carries a sense of _precariously balanced forces._ Something is going to change _because_ too much pressure or strain is building up. It will be a sudden and chaotic change. Yes, a natural context would be "Things just can't go on like this, something's gotta give." There's always an implied idea "but I don't know what it will be." It always helps to Google for examples of use. Here are a few. "Something's gotta give as San Francisco 49ers pass offense meets Giants pass defense." --these are too football teams and the headline writer things the game will be interesting because a team with a strong offense is going to meet a team with a strong defense. This is the "balancing forces, one must win" meaning. "Considering the trend, Apple might even choose to forego full-sized USB ports in favor of the same Type-C that it is pushing with the new MacBook. After all, if the MacBook Air is to be any thinner than it already is, something's gotta give." This is saying that making the laptop thinner is going to force Apple to leave something out. There won't be room for everything. "Something's gotta give." The writer thinks the weak point is the USB ports, and that's what will "give." "Miami Beach at 100 [years old]: The sea is rising, and so are the condos. Something’s gotta give, right?" Another "unstable balance of forces."

Can you explain the context of this sentence?