I think the other posters here have this well in-hand, so I have very little to add.
Remember... your LAN (or Local Area Network) is the
internal network in your home. It can run at ridiculous speeds compared to your internet connection. For instance, I have a 20-megabits down and 5-megabits up internet connection through a cable modem (that means I can download at a max of 20 megabits-per-second, and upload to the internet at a max of 5 megabits-per-second).
The internal LAN in my home is hard-wired Gigabit ethernet... which can theoretically run at 1000-megabits-per-second. That internal network is what carries all the camera streams to the NVR, and it has enough bandwidth that it carries that load easily, in addition to other traffic (audio streams from the internet, Youtube videos from the internet, various PCs backing themselves up to LAN storage, etc).
When I want to get to the internet, the request goes from the PC I'm seated at, across the LAN to the router (mine is custom-built by me, but yours might be a standard Linksys, Netgear, Belkin, D-link, etc), from the router to the cable-modem, and out to the internet. That's the only time the bandwidth of the internet connection comes into play. The internet connection is the bottleneck in 99% of homes (my internal network is many times faster than my internet connection)
If I'm accessing my camera system remotely, the internet connection ALSO comes into play, since I only have 5-megabits-per-second of upload pipe. This means I can't get full-motion on every camera on my system (which is quite large). I can get full-motion on maybe ONE... and stop-motion on most of the others.
None of that affects what's going on within the LAN... that continues unabated, regardless of what I'm doing remotely. That means the cameras stay running, the NVR keeps recording, and everything goes on as-is.
The "internet connection speed" only comes into play when you're talking about remote access.
Make sense?