Generally when people talk about going to/graduating from university, they're talking about an undergraduate degree. It's the one you take after secondary/high school. You may have also heard it being called a bachelor's degree. You need one to get a graduate degree.

A graduate degree is either a master's degree (above an undergraduate degree) or a doctorate (above a master's degree and the highest degree you can get). They're called graduate degrees because you already have your undergraduate degree.

So it goes high school < undergraduate < graduate.