What mean on-demand scanner or on-demand scan?
A scanning that you ask to be done.
Not automatic when you run, execute, open, create, modify a file. This is on-access scanning.
On-demand is a scanning of the system that you order (or schedule) 
Exactly !
And also, it can not be rephrased better and more appropriate than it already is… ON DEMAND SCAN… SCAN that is activated ON my DEMAND… just when I want avast! to perform those scans…
As Tech already mentioned, ON ACCESS SCAN means, when all those files are accessed, they will be scanned… and most important, it’s a resident task, so it means, it’s sitting in “background” and protecting your computer while you are doing something else… It helps you keep your computer pet well protected. ;D
Cheers !