This quote, said by Eowyn in the film version of the Lord of the Rings, is actually said by the character Faramir in the books by J.R.R. Tolkien. Tolkien stated that he included this dream in his books from his own personal experience which was also passed on to his son. Both father and son had dreams of great waves of destruction, what Tolkien referred to as his "Atlantis Hauntings".
 
I too have had these dreams of great waves on more than one occasion. I personally feel they are portents of things to come; maybe not literal waves, but something overwhelming just the same.