A watermark is a company, photographer, or photo agency's way of marking its images for copyright, showing that that entity owns the image, and prevents the easy copying or reuse of that image, without legal permission. It is called watermarking, because of the technique that used to be used to make the marks.
The marks can cover up parts of the image, particularly, if the agency is very guarded, important parts of the images, such as a person's chin, because, although this is not the main focus of the image, it is nearly impossible to crop the picture down to remove the watermark while keeping the image. This is why pictures without watermarks are considered "better".
However, even pics without watermarks are generally still copyright-protected, so discretion should still be applied when taking them from another source.
This is the longer-winded and more technical explanation, but for a visual explanation, check out Crisinaki's post.