Running it as a service means BI loads/runs when the computer boots up. If you have a power outage, for example, and your system is set to boot up when power is restored, BI will automatically start up.
Blue Iris options, Startup tab, check "run as a Windows service". Do you have Windows 10? I think there are issues with Windows 7 running as a service, I forget what it was, I'm sure others will chime in.
I run my BI as as service. It runs in the background and starts running when windows loads. I run a headless machine and I don't need to log in since it's running as a service.
As others have said, running as a service means Blue Iris starts running when Windows boots up. If Blue Iris crashes for some reason it restarts when running as a service. You can open an instance of Blue Iris on your pc and do whatever you want, close it and Blue Iris is still running in the background.