What is the difference between printed, damask and jacquard tablecloths?

A printed tablecloth has the design printed on top of the fabric. The underside of the cloth will be plain.
In a jacquard, damask and matelassé tablecloth, the design is woven into the fabric. The threads (or yarns) are dyed before being woven, and the weaving is what makes the design appear. If you turn over a damask or jacquard tablecloth, you will see the same design in reverse. These tablecloths cost more because they use more time, energy, and labor to produce. They also have a silky hand, and tend to hold up very well and last a very long time. Damask and matelassé designs are traditional and formal and are usually solid color. Jacquard typically use many vivid colors.