So what exactly is this doing in the background?

Hello Reads59,

Rapid Security Response updates are a relatively new feature of the Apple ecosystem. It allows for Apple to push important security updates to your Apple devices (iPhone in this case) without needed to do a full iOS upgrade. When updating via Rapid Security Response you could've noticed how fast it updated as opposed to an iOS update.

It is doing nothing in the background! Think of it as a really fast and easy way for Apple to fix vulnerabilities on your Apple devices! They should all be very quick meaning you can get right back to doing what you were doing! It also allows Apple to update vulnerabilities they find quickly and push them out quickly.