HTTPs is an encrypted connection between the server and the computer that is connecting to it, to consume and post information. This encryption is done via an SSL certificate. This certificate is verified by a trusted organization and ensures that the website you are interacting with, is indeed legitimate, as its owners and trustworthiness has been verified and vouched for by Certificate Authorities (CA's), usually authoritative security firms such as Comodo Security and Symantec, amongst others.
When properly implemented (not all HTTPS connections are actually fully secured), HTTPS connections protect you against so called 'Man in the Middle attacks', where third parties (like governments, hackers) are secretly listening in on the information you send and receive. Think of passwords you type in or sensitive information a website may try to send you.
Boring, you say? Or maybe you feel that your website doesn't transmit sensitive information (but remember you do have an admin account that, if fallen into the wrong hands, could lead to a total loss of content or hijacking of your site). Well, maybe the following post on HTTPS from Google could spark your interest. In it, the search giant announces that websites using HTTPS get a slight ranking boost over those websites that don't employ an encrypted connection.
What is also great to know is that SSL certificates, since they need to be verified and periodically renewed and re-vetted, cost money. But for our customers, we are happy to throw them in for free. Since we too share Googles sentiment that privacy and security are important. We should constructively contribute to the world wide web, after all, it is our working grounds.