Feedly enabled HTTPS for all its users a while ago, but there is no way to turn it on permanently on its website.
If you use Feedly’s app for Chrome, right-click on the icon, go to Options and enable HTTPS.
If you don’t use the Chrome app (or you use another browser), simply bookmark and use https://feedly.com.
HTTPS provides a secure connection between your computer and the website you’re visiting, and prevents others from eavesdropping on your browsing activity (which is why websites for banking and transactions use HTTPS). You should turn on HTTPS on every website that supports it.