When working with materials in three js many of the materials support one or more types of maps for skinning the faces of a geometry one such map is an alpha map. An alpha map is a gray scale texture where white areas of the texture will result in a face being fully opaque while black areas will result in the face being fully transparent.
So for a basic example of an alpha map in three js I have this example that makes used of a texture that is created from a canvas element. I just create a canvas and then make gray scale areas of the canvas, I then used the THREE.CanvasTexture constructor to create a texture that I can then use with the alpha map property of a material that supports alpha maps such as the Mesh basic Material.
The transparent property of the material also needs to be set to true, and a renderer that supports transparency also needs to be used. The usual webGl renderer worked just fine fr me in this example.
There are a whole bunch of different maps to be aware of when it comes to skinning faces of a geometry with a material in three js. There is the plain old color map that can also be used, and it materials that respond to light sources there are many other maps of interest as well such as an emissive map. Still alpha maps are one ogf the many types of maps to be aware of, and they can be fun to play around with.