Use this expression when you want to talk about two different things. The first thing is big or important enough. However, the second thing is even bigger and more important. Here are some examples:

She's not only super smart, but also hard-working and easy to get along with.

Kids who learn martial arts gain not only strength and fighting skill, but confidence as well.

The sentence doesn't always need "but":

I've not only been there, I've actually lived there for three years.