A profile gauge is an inexpensive device with sliding pins that are pressed on a surface to copy its shape. They are occasionally useful for general DIY, but have a use in woodturning too. The obvious use is in copy turning, when they make a template to exactly match the shape of a curve on two items. I have had one in a drawer for many years without using it very often. But I recently started getting it out a bit more often to use as a teaching aid.
A profile gauge shows the curve
When making bowls it is important to get good curves on the walls and bottom. I am a bit of a perfectionist and go to a lot of trouble to get them right on the bowls I sell. You can see the outside profile of a bowl easily enough. But the interior is more difficult, both to turn with the necessary accuracy and to see the shape. If the bowl is small enough, your fingers will tell you when you have it right. What you can see and feel is normally all that really matters in the finished bowl. But when the bowl is too big for your fingers to reach to the middle, you must rely on sight and/or calipers. Sometimes mistakes are missed during the turning. They show up later when the bowl is off the lathe and polished. They can spoil the piece.
Now I sometimes use a profile gauge to show the student in my woodturning classes how the shape of a piece is developing. The profile gauge shows the curve in two dimensions instead of three. Any flats, dips and bumps can then easily be seen. They are especially useful for the shallow curve in the bottom of the bowl, where the gauge will clearly show if there is a bump or dip in the middle. The best kind to get is one with thin metal pins, not thick plastic ones without the resolution needed.