What is a regex?
At its most basic level, a regex can be considered a method of pattern matching or matching patterns within a string.
Using Regular expression is a powerful way of making your SharePoint workflow string lookup easier with much less lines of code.
In a SharePoint workflows, the evaluation of whether a value matches your regex is done by the regex engine in the .NET system.
Here are some useful links that will get you started in using Regex.
Get Started wit Regex: Basic Regex Tutorial
This web tools helps you write and validate Regex: Regex Tester
Here is a .Net Regex CheatSheet : Cheatsheet
SharePoint Designer using Regex: Regex Workflow Samples