Q:

What's the meaning of "to wave someone on"?

Please explain to me what "to wave someone on" as in the below situation means. I cannot find the explanation on other dictionaries. Thanks a lot!
"Did you hear me?" Hazel demanded. "We're in a lot of danger"
The policeman stepped back from the car. "I said, you better get on home."
"You're not from around here, are you?" she asked him. "I mean you weren't born here."
He looked back at her, uncertainty in his face for the first time. Then his eyes hardened and he waved them on.

A:

The literal sense is that he waved his hand to indicate that they should proceed onwards. However, the actual waving isn't significant - the phrase conveys the meaning that the policeman indicated that they should move past him.

From definition 2 (verb) of wave:
  If you wave someone away or wave them on, you make a movement with your hand to indicate that they should move in a particular direction.
  - reverso

