In 300 Rise of an Empire, what do the sea serpents represent? Are they meant to symbolize something or is it a random piece from mythology? If they are meant to be from greek mythology, what are these particular sea serpents called?
The movie "300 Rise of an Empire" isn't about accuracy but about action. It is inspired by greek history but it is not a historic movie.
Even from the prequel the movie "300" Zack Snyder tried to create a movie that doesn't obey any law, physical, logical or historical. I personally like the movie but we must not try to explain it logically and in depth because it is based upon a comic.
So to answer your question the purpose of the sea serpent it to create a more "powerful" scene and to make the movie move intense. There are fights and naval battles and it adds to the action the emergence of a sea monster (while totally useless in my opinion). There was no reason for that serpent to be there and I personally think that he tried to exploit visual effects even more than in the prequel. While in the prequel you could think that we are still in a real world in this movie there are a lot of elements that just don't belong there!
The "300" was an excellent action movie and without these extreme and useless monster scenes that exist in the sequel. So he saw that it was a hit and tried to add even more fantasy things into it. That is a reason that this movie wasn't such a success as its prequel.