Wildcards have been around forever. Some even claim they appear in the hieroglyphics of the ancient Egyptians. Wildcards allow you to specify succinctly a pattern that matches a set of filenames (for example, *.pdf to get a list of all the PDF files). Wildcards are also often referred to as glob patterns (or when using them, as "globbing"). But glob patterns have uses beyond just generating a list of useful filenames. The bash man page refers to glob patterns simply as "Pattern Matching".
First, let's do a quick review of bash's glob patterns. In addition to the simple wildcard characters that are fairly well known, bash also has extended globbing, which adds additional features. These extended features are enabled via the extglob option.