Within the context of Chrome and other Chromium based web browsers, this means that Google will be able to monitor your web browsing in a new way any time you’re using a browser based on Chrome/Chromium.

With only slight hyperbole, we can say that Google can do this monitoring already.

What's worse, is now they can:

• Refuse you access to information by refusing to attest your environment.
• Restrict your browser, extensions, and operating system setup by refusing attestation.
• Potentially bring litigation against you for attempting to circumvent DRM (in the USA it's illegal to bypass DRM).
• Leverage their ad network to require web site operators to use attestation if they wish to serve ads via Google. AKA force you to use Chrome to use big websites.
• Derank search results for sites that are not using attestation.

In my opinion, the least harmful part of this is the ability to monitor page access, because they can more or less do this for Chrome users anyway. What's really harmful here is the potential to restrict access to and destroy practically the entirety of the internet.