Web monitoring?

I get an Avast popup telling me “Anyone can monitor and log your internet activity” when I visit certain webpages like my bank, clearly trying to upsell me on a VPN solution or the like.

My question is, well, what exactly is Avast monitoring and recording? While this is probably just a trigger on the domain name, it has me wondering what else it might be doing that I don’t know about. Is it sending any record of my activity back to their network? Is there some other log tracking network activity? Call me paranoid, but I’m not a fan.

http://www.avast.com/privacy-policy
https://forum.avast.com/index.php?topic=95250.msg759717#msg759717