Assist springs have two functions. The first is the spring adds a progressive rate to the initial portion of the stroke. This progression can add increased comfort is used on a daily driver coilover setup that has stiff springs installed. It provides racers added softer spring rate progression. Once the assist crushes, the normal spring rate will take over.
The second job is the same as helper springs. They prevent the loss of traction during rebound, and extreme cornering.

Assist springs are designed to repeatedly be fully crushed. Every assist spring crushes to the same height. That allows drivers to change assist springs without resetting the spring perch on coilover without changing ride height.