"Onboarding" experience is how we introduce the user to the product and its features. It starts with the website before the installation, includes first run experience, but is also an continuing process. After noticing that the user has used the browser 100 times, but never used tabs, we might tell him about it.
It's a very difficult balancing act. On the one hand, we want users to know about our features (and our newest cool feature is the best thing since sliced bread), but on the other hand, we want an easy and hassle-free experience without fuss and interruption. We need to consider power users who have installed Firefox many times on many of their devices, and people that barely know how to use a touch screen.
The idea of onboarding is to consider all these cases and create a good user experience for all of them at the same time.