Could someone explain to me exactly what these terms represent/mean and a breif description of how they are practised and there goals within the Yiquan system?

Thanking You in advance.

Shili is seeking or sensing force.
Fali is issuing force.

Shili is seeking out the structure to commute force across the body, from one point to another. It then enables you to use more unified body force to exert as strength instead of localized effort. Opening and closing, lifting and pushing, pulling and prying.. etc. You learn to do all of that without localized force. One funny thing about shili is how you need to learn to go in two directions at once.

Fali is essentially the same exercises, only done quickly and with an explosiveness. As there is a spring feeling in shili, fali is suddenly stretching that spring as to break it. Fali relies on the structures found in Shili (and Zhanzhuang) to suddenly snap into place to exert a large amount of energy. All strikes, kicks, and even grapples in yiquan use fali.