Full Idea
The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains.
Gist of Idea
The main quantifiers extend 'and' and 'or' to infinite domains
Source
Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5)
Book Reference
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.41