Here 'yet' means "but' I slept for ten hours, BUT I still felt tired the next day. You can also rewrite it this this, "Although I slept for ten hours, I still felt tired the next day."

You slept 10 hours, which is a long time. Yet means that even though you slept for a long time you are still tired for some reason.

You can seek it on the internet, I mean everything can be found on Google... Now since you asked, I won't leave without answering. In the sentence 'yet' means ' but nevertheless'. Good Luck ^^