Yes, regex is Regular Expression.
It is a complex search methodology that you've been using in it's simplest form every time you perform a search of any kind, anywhere. But most of the more complex stuff has been hidden; handled behind the scenes for you by whatever program (or website) you are using.
I recommended a Mac application that allows bulk file renaming with regex support simply because it can do lots of changes if necessary and, with some practice, handle almost anything you might come across. No matter how strange.
Take a look around the
RegexBuddy website for some examples on what regex can do and how to program it. This is a Windows only program meant to help teach and create regex expressions.
Regex comes in several flavors, depending on how a programming language implements search functions. Most of the stronger programming languages have their own version of regex. So there is python regex, C regex, etc. They're generally pretty close in syntax. Calibre uses python regex.
If you look through the various topics here in the calibre foums, you will find that their are a lot of regex expressions scattered about. Here are two regex topics:
Tyrannasaurus Regex
More fun with regex / wildcards