Well we would need more information to be able to say with any certainty what is happening.
The avastSvc.exe is the main scanning control and the Web Shield (and others) are controlled by this process. The web shield monitors your http traffic, to be able to do this and scan the content it redirects your browser http traffic through a local host proxy.
So depending on where you are seeing this, it could simply be that redirected traffic, so you see it under avastSvc.exe rather than seeing it all under your browser. This assumes that it is the web shield and not one of the other shields, such as P2P or Mail Shield, etc. See image example of my firewall log, click to expand.