What does a double colon followed by an equals sign (::=) mean in programming documentation?

It symbolizes ‘symbol derivation rule’ in Backus–Naur Form

Meaning that in:

<symbol> ::= __expression__ 

nonterminal <symbol> consists of (is defined as, is constructed from, derives from) __expression__

It’s used to describe language grammars.

Notice that both examples are in Extended Backus–Naur Form, but using a traditional BNF symbol-expression separator (::=).