Binary images (black and white) are everywhere in ImageJ, they are required in Analyze > Analyze Particles, have their own operators and functions.
This post explains what they are and how to use them...
Mathematical morphology (MM) [Wikipedia] is a great toolbox for image processing. In ImageJ, most of these operations are available for binary images and are often used to prepare an image before analysis. Moreover, the same operations can be used for gray-level images offering new functionalities in terms of filtering, segmentation,etc.
When playing with binary images in ImageJ, that's not
really simple to remember if TRUE corresponds to white or black
(specially, if you use a lot of different binary functions). Here are simple examples to try to understand how it works.