Are you specifically talking about Avast Internet Security? Or just internet security as a general concept?
In the case of Avast Internet Security (in case that's what you were referring to) you are protected by Web, File, and Email shields as well as an active Behavior Shield which monitors processes/etc in real time for malicious activity. In addition, we have CyberCapture which helps to catch zero-day or unknown malware downloaded from the Internet.
Depending on which shields you choose, you're protected in a variety of ways, from active file scanning to URL checking to behavioral monitoring, all of which is backed by our threat labs' streaming updates as well. More info here: https/www.avast.com/nextgen
If you have any additional questions about us specifically, I'm happy to help! But in general, any good security suite should help prevent and detect a variety of malware including ransomware and zero-days.