Stencils
Stencils provide a way to control which pixels will actually be put on the screen.
A stencil has 2 stages: first the stencil needs to be written or modified in some way with some kind of material that modifies the stencil. Then secondly, the stencil is tested by another material. This is usually some kind of comparison on the stencil value to make sure that we can or cannot write a specific pixel.
More information about stencil testing can be found here
Stencil Mode
Determines the mode of the stencil.
The 'Simple' mode provides stencil options that act on all the faces.
The 'Front & Back Face' mode provides separate stencil operations for the front and the back faces, letting you do more complicated stuff (like masking a hypno focus to only show up on the back faces - that is the inside - of the material)
When using the 'Front & Back Faces' mode, you'll have to lock the material to see the effects of it!