They tell you that the end-point of the encrypted transfer is controlled by the same computer or people that control the domain name. Assuming that neither your computer nor the server has been compromised in some other way, the data exchanged cannot be read, changed or replaced, and it is going to the right place. (That's a stronger than merely saying it can't be viewed.)
But of course it doesn't tell you that the address you think you are using is the correct one, or that the target server hasn't been taken over by hackers, or that there is no security bug in your browser, or that the certificate signing keys have not been stolen. As an internet user, you need to apply the level of paranoia you think appropriate.
I fully agree that search engines could be better in all sorts of ways. And I agree that it should be practical to do better in some ways at least, though I don't think there is any simple and general solution. And I don't agree that this has anything to do with SSL or certificates. (Topic drift is, as we know, the norm for this group. But you might want to separate it a little and give this a new subject line.)