"Bitter end" is an English idiom that is used to describe the very limit of a person's effort in a certain situation. It can also be used to refer to the persistence of the person it is describing, since he or she is willing to stick things out to their conclusion. The phrase "bitter end" has a negative connotation, implying that something is not going to end well. Although there is some evidence that the phrase has nautical origins, it most likely plays off the figurative meaning of the word "bitter."
There are times when the English language affords speakers the opportunities to add some color and impact to their words and phrases. Idioms are examples of this colorful speech, since they can often evolve to mean something much different from their original meanings from when they were first spoken. Popular usage of these phrases transforms their meanings into something that everyone in the culture comes to understand even if those meanings aren't indicative of the literal meaning of the words. One of these idioms that has survived for hundreds of years is the phrase "bitter end."
When this phrase is used, the implications are that someone is willing to stick through something even if it's uncomfortable or unpleasant. Only when the event in question is finished will the person relinquish his or her commitment to it. It's a sign of persistence, even if the eventual result will be negative. As an example, imagine the sentence, "I've watched two hours of this awful movie, and I'm going to stick with it to the bitter end."
In any case, the phrase seems to imply the very boundaries of the tolerance someone has for something. The connotation of the phrase is almost always negative, as may be inferred from the tone of the word bitter. When someone reaches this limit, the end result is usually a culmination of all the indignities suffered to that point. For example, someone might say, "I've dealt with so much already, but here I am, at the bitter end, ready to deal with whatever else might happen."
Some anecdotal evidence exists that connects this phrase to the old-fashioned sailing practice of tying a rope around a post. It's more likely that the phrase gained its meaning from the way the word "bitter" is often used. Whereas the word literally refers to a sour taste, it often has a figurative meaning that describes an outcome that is very difficult to take.