There are times when we have to deal with gray areas, instead of binary-based values, to make decisions, and fuzzy logic is a set of mathematical techniques that help us with this task.
Imagine that we're developing an automated driver. A couple of available actions are steering and speed control, both of which have a range of degrees. Deciding how to take a turn, and at what speed, is what will make our driver different and possibly smarter. That's the type of gray area that fuzzy logic helps represent and handle.