What is pattern group? What are pattern groups used for?

How to write a regular expression using groups to capture character names from the Ed, Edd 'n' Eddy animated comedy television series?

The grouping mechanism allows a part of a regex to be treated as a single unit. A group is represented by regular expression pattern enclosed in parentheses like this: (...).

Groups can be used to capture sub strings in a matched pattern. For example:

\D*(\d+).* # a group to capture the first string of digits 
\W*(\w+).* # a group to capture the first word

Groups can be used to limit a logical OR operation. For example:

(Mon|Sun)day.* # Excluding 'day.*' from the 'Mon|Sun' operation

Groups can also be nested to form a complex groups. For example:

house(cat(s|)|) # matches house, housecat or housecats

The regular expression to capture all Ed, Edd and Eddy is:

Ed(d(y|)|)

(y|) - inner group to match 'y' or nothing
(d(...)|) - outer group to match 'd(...)' or nothing