'Going to the girls' room' is a euphemism for 'going to the toilet'.

Literal

''Girl [possessive-の] room [to-へ] go'' [quotative-というのは] ''toilet [to-へ] go'' [quotative-ということ] [possessive-の] euphemism is.

A linguistic/cultural note about euphemisms. 婉曲表現 (えんきょくひょうげん) is the technical term for 'euphemism' — literally 'roundabout expression'. The quotative nesting is notable: 「A」というのは「B」ということの婉曲表現 = '"A" is a euphemism for the concept of "B"'. ~というの turns a quoted phrase into a topic. ~ということ turns a phrase into an abstract thing.