A postscript (P.S.) is an afterthought, thought of occurring after the letter has been written and signed. The term comes from the Latin postscriptum, an expression meaning "written after" (which may be interpreted in the sense of "that which comes after the writing").
A postscript may be a sentence, a paragraph, or occasionally many paragraphs added to, often hastily and incidentally, after the signature of a letter or (sometimes) the main body of an essay or book. In a book or essay, a more carefully composed addition (e.g., for a second edition) is called an afterword. The word "postscript" has, poetically, been used to refer to any sort of addendum to some main work, even if it is not attached to a main work, as in Søren Kierkegaard's book titled Concluding Unscientific Postscript. Sometimes, when additional points are made after the first postscript, abbreviations such as PSS (post-super-scriptum), PPS (postquam-post-scriptum) and PPPS (post-post-post-scriptum, and so on, ad infinitum) are used, though only PPS has somewhat common usage.
Historical examples
On February 14, 1815, a letter written by Thomas Jefferson, the third President of the United States and main author of the Declaration of Independence, used the P.S. abbreviation to add a lengthy postscript, which he dated February 26.