More specifically, as far as I know, it's the penny you would use in a pay phone before everyone had mobiles. You'd put it in the slot and a mechanism would lock it. Press the release button, and you'll get it back.
When the other person answers the call, the mechanism releases your coin into the phone's "safe", and you can hear the "clink" sound as it hits the other coins. That kind of tells you that it went through.
Thus, when you make a call on a pay phone, when the other person finally picks up and a connection is made, the penny drops.
It's never in the air though, it's locked in that mechanisn.. I reckon the only time I heard "penny in the air" was in Doctor Who.
And in my country we say "the phone token drops".