Literally, a running or passing between. Hence,

Communication; commerce; connection by reciprocal dealings between persons or nations, either in common affairs and civilities, in trade, or correspondence by letters. We have an intercourse with neighbors and friends in mutual visits and in social concerns; nations and individuals have intercourse with foreign nations or individuals by an interchange of commodities, by purchase and sale, by treaties, contracts.

Silent communication or exchange. This sweet intercourse . Of looks and smiles.