[regex] What is a non-capturing group in regular expressions?

HISTORICAL MOTIVATION:

The existence of non-capturing groups can be explained with the use of parenthesis.

Consider the expressions (a|b)c and a|bc, due to priority of concatenation over |, these expressions represent two different languages ({ac, bc} and {a, bc} respectively).

However, the parenthesis are also used as a matching group (as explained by the other answers...).

When you want to have parenthesis but not capture the sub-expression you use NON-CAPTURING GROUPS. In the example, (?:a|b)c