I believe they're discribed in the help
Shortly, they are digital signatures of the mail message, written there by an avast! scanner. This proves that the message has been scanned on the way. (Not like the usual inserted notes "message scanned by..." - theoretically, anybody can write such a foot to his/her e-mail message, without any relevance to the actual scanning).
The note about the "minimizing the number of scans" means that if there's some other avast! scanner on the way (either the sender of the message uses it, or the mail server you are using is running avast) - then your avast! e-mail scanner doesn't have to scan the message again (when you receive it) - if it was already scanned and signed.
I'd say it's not very likely to help you much (currently).