What does Harness mean?

A frame used for holding heddles which allow for warp yarns threaded through its eye.

Heddels explains Harness

The harness, or shaft, refers to the rectangular frame of the loom to which all the heddles are attached. A basic loom has two harnesses; however, looms can have up to sixteen harnesses. The more harnesses a loom has, the more design possibilities are available. Denim, a twill-woven fabric, requires a loom with at least four harnesses.

Additional Resources

Here is a picture of a harness: