Wigglers are used to assist in the centering of work held in the 4jaw or faceplate. Typically, a long rod pivots off-center on a pivot point held in the tool holder. The short end of the rod goes in a hole-to-be-centered in the work. The long end points at a center held in the tailstock. As the work is rotated by hand its offset center makes the short end of the rod describe a circle. Because of the lever effect the long end then describes a much magnified circle around the TS center. Adjustments are made to null out the circling of the long end and this centers the work.
If you've just finished building a lathe ball turner, the top one is for you. The brass ball can be slid along the rod to change the magnification. The ball seats in a conical dpression in the hexagonal ring.
The bottom one is a somewhat different design but easier to build since no ball turning is required. Same principle but the magnification factor is fixed.
The one in the middle is my personal favorite. It's called a "pump" center. The male end goes in the work and the spring-loaded female end is supported by the tailstock center. A DI held in the tool holder bears on the portion of the rod close to the work and makes it trivial to center the work if you use my centering technique documented elsewhere.