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".
"This legend or myth or dim memory of some ancient history has always troubled me. In sleep I had the dreadful dream of the ineluctable Wave, either coming out of the quiet sea, or coming in towering over the green inlands. It still occurs occasionally, though now exorcized by writing about it. It always ends by surrender, and I awake gasping out of deep water. I used to draw it or write bad poems about it."
– J.R.R. Tolkien, Letter 257
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.