Regex stands for 'regular expression'. But what are regular expressions? Simply put, they are patterns used to match (find) sequences of characters in a string. You could use regular expressions to match whole words, parts of words, or more complex patterns such as numbers beginning with a '£' symbol.
It is worthwhile having some familiarity with regex because it crops up in so many different contexts. Google Analytics, for example, supports the use of regular expressions in filters, goals and segments.