Barrel rotation is very easy to understand. It's just a rotation of the pen along its long axis.
In the diagram below, barrel rotation is indicated by the arrows that go around the long axis of the pen (as indicated by the dotted line).
Barrel rotation is a very rare feature on pens. I know of only three pens that support it.
Wacom Art Pen (KP-701E)
Wacom 6D Art Pen (ZP-600)
Apple Pencil Pro
Keep in mind that these pens only work with specific tablets. You cannot buy these pens and assume they will work with the tablet you have.