Yahoo! and gmail are web-based email portals. They use your browser to access their servers and download email content.

Outlook, Thunderbird, and the like are email programs you install on your system.

avast! Mail Shield does not work with web-based email, but is designed to work with installed email client programs.

You can safely remove Mail Shield without impacting your use of Yahoo! and gmail. It’s not needed if you use web-based mail.