The actual, physical thickness of a piece of paper, usually expressed in thousandths of an inch, is the caliper of the paper. Caliper affects the flexibility of paper and desktop printers can have difficulty with papers that are too thick or bulky.
Paper weight and thickness (caliper) may have little or no noticable effect on printed image quality. However, heavier, thicker papers feel more substantial and can lend visual weight to a project. In the case of extremely thin papers, however, heavy ink coverage can result in bleed-through.
Higher caliper papers hold up well when there is heavy ink coverage. For full color photos from your desktop, thicker inkjet photo papers are best. However, some desktop printers may not handle thicker papers well, especially if the printer doesn't have a straight paper path. The same is also true of papers with a very thin caliper. Bible papers used for some Bibles, dictionaries, and product inserts and tissue-like onionskin papers are can easily wrinkle and cause paper jams in some printers.
Caliper also refers to an instrument used to measure caliper or thickness as well as distance.