From a strict point of view, a “word processor” is little more than a fancy electric typewriter where you can edit the content over and over. It's probably designed for printing the documents that you type, but that's not mandatory (it's quite feasible that documents might be produced just for viewing electronically).
A really simple “text editor” has these features, too, but generally lack the extra things neceessary considered necessary for writing documents (e.g. spell checkers, formatting of blocks of text into headings, lists of items, paragraphs, etc.), only offering the ability to handle text on a line-by-line basis (which doesn't allow for typing new material into the middle of a line, with the remainder of paragraph reflowing around it neatly.
A word processor's chief job is to let you type an article, and change the contents as necessary, though they often offer extra features. Most include basic typing aids, such as spell checkers, and simple margin and page layout features, but once they start to do things that couldn't be done with an ordinary typewriter (e.g. include images and diagrams, etc.), they cross over into the field of desktop publishing (though often being inadequate at the task). If you're trying to do a job that needs layout control (e.g. magazines, newsletters, flyers, brochures, etc.), then you really should use a desktop publishing type of program, instead of a word processor.
This is a small-scale equivalent of a printing press on a personal computer. Whereas a word processor is chiefly aimed at being something that can produce a document, “desktop publishing” is about laying out things on pages (it may be a single document, it could be several separate articles in a single publication, and can include images and diagrams).
You have full control over what's printed on a page, where it's printed, how it's printed, and how printing is handled over multiple pages (e.g. articles that span different pages, the layout of an entire magazine or book, etc.). Generally, objects (images or text) are placed in certain positions on the page, and fitted into the space allocated to them. This means that you can do things like alter the text of an article without displacing other objects on the page, or you can add images to a page, and flow the text around them in a sensible manner.