Turn on that checkbox in case if your instance of Jenkins is not accessible from GitHub where you have pull requests.

When that option is turn on. Instead of link to Jenkins hosted icon, Jenkins publishes coverage icon to Pull Request as img from http://shields.io

More info: Plugin publishes coverage icon to Pull Request. Icon is a link to picture which hosted by Jenkins. When user opens Pull Request, GitHub tries to get icon from Jenkins server to show it to user. Depends on location of Jenkins and GitHub it could be a case when link on icon published by Jenkins is not accessible. One of example when you are using public github.com however your Jenkins in internal network and not accessible from internet.