I always think Regular Expressions as a way to express a set of things. I think they are a way of expressing the set of all possible characters that follow a certain set of rules. Imagine writing code to determine whether a given address of a country is valid. One can use regular expressions to form a pattern that uniquely identifies addresses among pieces of text or among large paragraphs.
It is all about pattern matching and I personally love pattern matching because I love thinking like a mathematician who generally finds and identifies patterns in almost anything in the world.
Regular Expressions are very fun to use and they can help instructors create challenging quizzes for students.
More over, Regular Expressions are used in compilers to detect valid or invalid syntax usage.
Speaking about the inventors of computers, which are humans, we often use regular expressions in our daily life.
For example, determining the location of a caller using the area code of their phone number, understanding whether a beta version of a software is in its final stage by checking the last character of its firmware number.
Personally, Regular expressions are the things that made my math class even more exciting and interesting. Some of the applications or usage of regular expressions include finite state automatons, deterministic and non-deterministic machines.