Ok, so while this high-level abstract discussion about Ko might be fascinating, I wanted to slow down, and just give you some idea of how a Ko threat might play out in an ordinary day-to-day 19x19 game.
I’m not going to use pictures this time. I’ve gotten into overly-deep waters doing that in my other Go-for-Beginners threads so I’ll just ask you to imagine the following situation in your head.
You are playing as Black - you’ve gotten yourself in a bit of a pickle because you were trying to extend a tendril out from your living territory and reduce White’s enclosure. White counter-attacked, and played in such a way so as sever the connection between your tendril and the living group. Exactly how it happened isn’t all that important - the important thing is that the place White cut you has this crucial shape at the crux:
Think of it as a binary bit that has two states - Advantage White and Advantage Black. White has just flipped that bit, so it’s Advantage White.
Black has a lot riding on the outcome of this because if White is able to fill in the blank space at A with another white stone, then Black’s stones are cut off from the living group, and White gets a huge lead. More than anything, Black wants to flip that bit the other way (Advantage Black) and then fill in the spot at B so that its tendril is connected to its living group. Doing that will give Black a big advantage because it will reduce White’s framework.
Because of the rules of Ko, Black cannot just play at A on the next move and capture White’s stone. Black HAS to play somewhere else. However, unless that move provides an adequate threat to White, White will simply fill in the gap at A, close up the shape, and capture the stones in Black’s tendril.
So, Black looks over the board for the places where it can play the most threatening move possible - something that will FORCE White to play there rather than close up the gap at A. One usual tactic is to peep at a big cut point or find a place where White has stones with only 2 liberties left and take one of those liberties away. Also, Black’s looking for opportunities where White would lose enough stones so that the loss of them would hurt White more than capturing the cut-off stones in Black’s tendril. These moves can be hopeless suicide moves - i.e. moves made knowing they will be captured on the very next move. Their main goal is to motivate White to play elsewhere.
So Black finds such a move and plays there. White is alarmed enough to play a local response to rescue whatever was threatened. Black can now come back and flip that bit to Advantage Black. Now the shoe is on White’s foot. Unless it plays something to capture Black’s attention, Black will play at B, connect its stones, keep its tendril alive, and reduce White’s enclosure.
So, White does the same thing - it finds the most threatening move it can, and tries to get Black to respond there rather than closing the gap at B. The gambit works, Black plays elsewhere, and White flips that bit back to Advantage White.
This back-and-forth situation goes on until one side or the other runs out of moves that are threatening enough to distract their opponent. Eventually, one side or the other will decline to play elsewhere after it has flipped the Ko bit to its advantage, and will seal the deal by closing up the hole and ending the Ko battle.
Now, this is a highly simplified situation. In lots of games, rather than playing hopeless moves that are immediately going to be captured, Player A can string together a series of Ko threats into an invasion or reduction in its own right. Alternately, the place on the board where the Ko is happening might have additional opportunities for capturing other pieces on either side, so that rather than just flipping one Ko bit back and forth, you might end up with a latice of 2 or 3 different bits which either side can flip over.
But yes, eventually, all such ambiguities will be settled one way or another based on each player’s willingness or unwillingness to play somewhere else given the relative risk of the two places in question.
I hope that clear it up 
