Shooting the messenger isn't really a way to go, e.g. Silent Mode.
These are alerts made by the Web Shield (made silent by your settings), so you don't know what the Web Shield is alerting for/on. It has prevented a connection to a site the browser/site has tried to connect to.
Because of the Silent Mode you don't see the actual Alert Screen, but the information is recorded in the Notifications. This alert screen provides a lot of information, e.g. what has tried to make the connection and the URL of the detection.
Without this kind of information it is almost impossible to offer advice other than switch off silent mode, so if it reoccurs you have information to give.
Which would be, a screen shot of the Avast Alert with the Details option selected and attached to the post.