One of the biggest complaints I see from webmasters about the Google Search Console is that messages you get about 404s or other issues that the webmaster is aware of, still keeps coming in. Webmasters who are aware of messages may decide to ignore them because they know better and they don't want to keep being notified of those issues.
Now, webmasters can unsubscribe from some of those types of messages.
Google announced on Google+ about the new feature:
1) When you receive a message you’d like to disable, click “Unsubscribe from this type of message” in the footer of the email.
2) Messages you’ve disabled will be listed in your Search Console preferences page - just like on the screenshot below.
3) You can re-enable messages from there as well.
Here is a picture of the interface:
I assume many webmasters will be happy about this feature.
Forum discussion at Google+.