A word processor, or word processing program, does exactly what the name implies. It processes words. It also processes paragraphs, pages, and entire papers. Some examples of word processing programs include Microsoft Word, WordPerfect (Windows only), AppleWorks (Mac only), and OpenOffice.org.
The first word processors were basically computerized typewriters, which did little more than place characters on a screen, which could then be printed by a printer. Modern word processing programs, however, include features to customize the style of the text, change the page formatting, and may be able to add headers, footers, and page numbers to each page. Some may also include a "Word Count" option, which counts the words and characters within a document.
While all these features can be useful and fun to play with, the most significant improvement over the typewriter is the word processor's ability to make changes to a document after it has been written. By using the mouse, you can click anywhere within the text of a document and add or remove content. Since reprinting a paper is much easier than retyping it, word processing programs have make revising text documents a much more efficient process.
The term "text editor" can also be used to refer to a word processing program. However, it is more commonly used to describe basic word processing programs with limited features.