It is always helpful to look at the context of a quote to understand the overall flow of thought. The analogies of the tree and the sailor, found in lines 712–717, follow and support the main point that is stated more plainly in lines 705–711. Here is my translation of those lines: Do not now carry in yourself one frame of mind only, that what you say, and nothing else, is correct. For whoever thinks that he is the only one who uses his brain, or thinks he, and no one else, has a voice or an opinion, these people, when they are opened up, are seen to be empty. But even if he is wise, it is not shameful for a man to learn many things and to not struggle too much to be right.

So, both the tree and the sailor are analogies, examples of things that live and survive if they give in, but are destroyed if they refuse to bend. In the same way, Creon is being exhorted not to insist that he alone is correct and not to remain so firmly fixed in his opinion of Antigone. As stated in the other answer, however, the king refuses to change his mind until it is too late.

This passage comes from Sophocles' Antigone and is found in a lengthy speech that Haemon makes to his father Creon, who is the king of Thebes.

Haemon is trying to persuade his father to be more flexible in his decision making. Creon has declared that Antigone, who is Creon's niece and Haemon's fiance, must be put to death.

In making his argument, Haemon draws upon illustrations from nature and from sailing. Thus, using figurative language about trees and sailors, Haemon tries to get his father to appreciate the strategy of "bend but don't break." In a storm, trees that don't bend and sailors who don't slacken their sails end up getting destroyed. On the other hand, trees that bend and sailors who slacked their sails remain intact.

So, Haemon is trying to get his father to be more flexible with respect to Antigone. Unfortunately for Creon, he does not decide to become flexible until it is too late. By the time Creon reverses his death sentence against Antigone, she has already killed herself.