Real-time shields basically scan any incoming data for malicious stuff. For instance if you clicked on a dodgy link, Avast! would automatically block it from loading the page. you'll get an information box like this:
Malwarebytes' only works if you run it, I recommend running it on all hard drives you have to look for anything that might have slipped past Avast!
Avast also has a whole bunch of other shields. Glancing at the Avast UI on my pc I can see
File system shield - monitors all files and folders on your PC
Mail shield - scans incoming and outgoing emails
Web shield - scans any webpage before it lets the PC accept any files from it
P2P shield - monitors any P2P programs (uTorrent, BitTorrent, Vuze) you might be using for malicious traffic
IM Shield - monitors file transfers from instant message programs (Windows Live Messenger, Skype, and so on)
Network shield - prevents any virus that might be present on your home network from getting into your PC
script shield - intercepts and prevents any malicious or damaging scripts being run locally or remotely
behavior shield - monitors system background processes and the like to watch for unusual behavior.