(covers information from several alternate timelines)
An aircar was a type of automobile designed for travel in the air. It was distinguished from other types of cars that drove on the ground, without any antigravs, and also from the hovercar, a similar vehicle limited to hovering over the ground; an aircar could take flight at much higher altitudes. Also, at least some aircars had wings.
In Paris in the year 2257, a number of aircars were flying in the sky when Michael Burnham was told about her pardon from the President of the United Federation of Planets by Sarek. (DIS: "Will You Take My Hand?")
In the alternate reality, an aircar flew over Starfleet Headquarters when Kirk and Spock reported to Admiral Pike following the incident on the planet Nibiru. A few aircars could also be seen outside Pike's office window. (Star Trek Into Darkness)
When Kirk and Pike went to Starfleet Headquarters, a number of aircars were flying by in the San Francisco skyline. One could also be seen from the window outside the Daystrom Conference Room, and after Pike's death, one flew by outside Kirk's apartment. (Star Trek Into Darkness)
In 2259 of the alternate reality, after John Harrison attacked the Daystrom Conference Room with a jumpship, some police aircars converged on the scene at Starfleet Headquarters. (Star Trek Into Darkness)
In 2364, when Jean-Luc Picard was visiting a holographic recreation of the Café des Artistes on the Enterprise's holodeck, a couple of aircars could be seen in the Paris skyline. (TNG: "We'll Always Have Paris")
The name "aircar" has never been stated in canon, but it is taken from multiple non-canon sources. While hovercars were designed for near-ground travel, an aircar could be useful for higher altitudes. Even though the name itself wasn't used on screen, vehicles matching the description of the non-canon aircars were shown.