Clustering is grouping, like in an algebraic expression. Parentheses limit how far back and forward an alternator (vertical bar) applies:

/foo|bar/;  # Matches "foo" or "bar"
/fo(o|b)ar/;# Matches "fooar" or "fobar"
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Grouping also allows quantifiers to apply to more than one atom:

/foo{3}/    # Matches "foooo"
/(foo){3}/  # Matches "foofoofoo"
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Capturing is storing the parenthesized portion of the match somewhere that you can refer back to it (as $1, or as an element of the list returned by a match, for example). Ordinary parentheses are capturing parentheses. Special parentheses (any that have a ? after the opening paren) are non-capturing. All parentheses group their contents.