Assist hooks are used for vertical jigging as well as with lures as a substitue for treble hooks. Assist hooks can also be used for a variety of other fishing applications. One very popular use is as a stinger hook, looped onto the hook of a bucktail. It's a great way to improve hook up ratio when gettting short strikes.
An assist hook is a j-hook that is rigged with strong spectra/dyneema/kevlar cord. The cord is secured to the hook and offers a loop of easy attachment to a lure or ring. For toothy species, assist hooks are made with wire or cable.
An assist hook solves a couple problems.
ONE: An assist hook eliminates jig to leader foul when vertical jigging. A jig that is rigged in a traditional fasion via split ring and treble hook has a common fouling issue when yo-yo or speed jigged. This issue will drive an angler crazy especially in deep water situations.
TWO: Fish can not use leverage to throw the hook like they can with a treble hook rigged on a lure. The flexible assist cord eliminates the possiblity and the j-hook provides a solid and secure hookset.