Using HTTPS instead of plain HTTP to connect to a website allows you to encrypt your communication with the server. But encryption alone does not guarantee that you are talking with the right server, and not someone impersonating it, for example in case of a man-in-the-middle attack.
But this trust system has proven to be flawed in many ways. For example, during 2011, two certificate authorities were compromised, and many fake certificates were issued and used in the wild. See [Comodo: The Recent RA Compromise](https://blog.comodo.com/other/the-recent-ra-compromise/)and [The Tor Project: The DigiNotar Debacle, and what you should do about it](https://blog.torproject.org/blog/diginotar-debacle-and-what-you-should-do-about-it).