Great question! The best example I know of is the `java.net.URL`class. As part of its `equals` function it resolves the URL to an IP address and uses that as part of its comparison. So, for example, if today you did the following comparison `new URL("http://example.com").equals(new URL("http://example2.com"))` and those two URLs pointed to the same server it would return `true` other than that being confusing where the consistency issue comes in is that lets say later example2.com moves hosting to a different server. Now running the same equality check would return `false`. Thus inconsistent. The data within the class is identical thus it should have the same result. The key point of that section is "don't rely on unreliable sources". In this case an external system, DNS, is that unreliable source. A random number generator was used as an example because it was immediately obvious the issue.
Hope that helps.