"small opening in the side of a ship to admit air and light," 1788, from air (n.1) + port (n.2).
Entries linking to air-port
air n.1
c. 1300, "invisible gases that surround the earth," from Old French air "atmosphere, breeze, weather" (12c.), from Latin aer "air, lower atmosphere, sky," from Greek aēr (genitive aeros) "mist, haze, clouds," later "atmosphere" (perhaps related to aenai "to blow, breathe"), which is of unknown origin. It is possibly from a PIE *awer- and thus related to aeirein "to raise" and arteria "windpipe, artery" (see aorta) on notion of "lifting, suspended, that which rises," but this has phonetic difficulties.
In Homer mostly "thick air, mist;" later "air" as one of the four elements. Words for "air" in Indo-European languages tend to be associated with wind, brightness, sky. In English, air replaced native lyft, luft (see loft (n.)). In old chemistry, air (with a qualifying adjective) was used of any gas.
To be in the air "in general awareness" is from 1875; up in the air "uncertain, doubtful" is from 1752. To build castles in the air "entertain visionary schemes that have no practical foundation" is from 1590s (in 17c. English had airmonger "one preoccupied with visionary projects"). Broadcasting sense (as in on the air, airplay) is by 1927. To give (someone) the air "dismiss" is from 1900. Air pollution is attested by 1870. Air guitar is by 1983. Air traffic controller is from 1956.
port n.2
c. 1300 (mid 13c. in surnames), porte, "a gate, an entrance to a place, a portal; the gate of a town or fortress," also in names of specific gates, from Old French porte "gate, entrance," from Latin porta "a city gate, a gate; door, entrance," akin to portus "harbor," from PIE root *per- (2) "to lead, pass over." Old English also had occasional port in this sense, from Latin, but the Middle English word seems to be a new borrowing via French.
The meaning "porthole, an opening in the side of a ship" is attested from mid-14c.; in old warships, an embrasure in the side of the ship through which cannons are pointed. The medical sense of "place where something enters the body" is by 1908 probably short for portal. In computers, "place where signals enter or leave a data-transmission system," by 1979, from earlier use in electronics (1953) for "pair of terminals where a signal enters or leaves a network or device," which also probably is short for portal.