What Are They For?
Telescoping gauges are for measuring the diameter of holes, the width of slots, and any other gap that is impossible to get calipers into. The standard model is T-shaped with the bar of the T composed of two sprung arms with round ends. The other end of the handle has some sort of locking mechanism. You stick the appropriate sized gauge into the hole, lock the arms, pull it out and then measure the result with a micrometer or calipers.
I say appropriate size because each gauge has limited range of measurement and thus telescoping gauges come in sets or at least collections. Mine is a motley assortment bought from a used tool store.
For small holes, there is a different style of gauge that is a split cylinder with a center plug that adjusts the split. I only have one of those.
There are digital and dial direct reading bore gauges which are the more precise but more expensive choice.
The basic import sets go for about $40CDN and cover a range like 5/16″-6″. You can spend more for better ones just like other measuring instruments but for the money a dial bore gauge set would be a better buy, I think. I don’t have one of those because I have not had cause to use my telescoping gauges enough to start wanting better.