These tools are designed to be used to check the depth of closed forms and open forms. These include bowls, platters, hollow forms, boxes and any other object you are working with on the lathe that you need to know where the bottom is to avoid going too deep.
The center hole is designed to be used with more open forms. Allowing both of the edges of the form to make contact with the depth finder. Once the depth rod is advanced down to the very bottom of the form, lock it in place and remove it from the form. now set the depth finder back on the face of the form, with the depth rod on the outside of the form. close one eye, and look straight down and this will give you a good idea of where the inside is in relation to your bottom. Using it on closed forms is the exact same process, you just use the hole towards the end labeled closed forms.
The varying sizes of the depth finder allow you to check forms that are both the diameter and the depth of the size range for the size given. These size correspond to the maximum depth and diameter that the gauge is designed to be used on.