A digital watermark is a kind of digital signature, usually in the form of a subtle modification to the main content of an image, audio, or video file. To put it another way, a digital watermark stores metadata inside the main content of a file, instead of separately. There are a number of different reasons for using a watermark, but the main point is to make it difficult to remove the metadata.
A digital watermark could be anything from a clearly visible overlayed semi-transparent copyright notice, to a steganographic technique that makes the signature virtually undetectable, or anything in between. It could be a simple notice of what software created the file, or it could contain detailed tracking information intended to help figure out who created the file.
Calling something a "watermark" usually implies that it is designed to survive at least minor modifications to the document.
Similar to bar codes, some kinds of watermarks store digital data in physical/analog documents. See Watermark (physical).