ashdisp.exe = icon on system tray
ashmailsv.exe = mail service
ashserv.exe = standard shield (resident) protection
ashwebsv.exe = Web shield provider service
aswupdsv.exe = avast update service
These are the ones that are 'running' in background.
When you start an update you'll see
avast.setup, when you run an on-demmand scanning you'll see
ashSimpl.exe running...
But, in fact, avast has only 4 services