It just means the thread has been dyed over - i.e. from its original color. Sometimes to make special effects, or sometimes just because the original colour wasn't right, or had faded. It's not just a cross-stitch term, but used of any thread treated in this way.
Overdyed threads have the characteristic of a gradation of tones of the color throughout the strand. Cross-stiching with this type of thread, by combining strands differently you can create a degree of realness or decorative highlight to the piece.