I allow my son to use the internet or cut him off by browsing to my wired router, logging on and filtering or unfiltering the MAC address of his PC. I noticed that there is a feature to allow remote management in the router settings which is not checked. How does this work? If I check the allow remote management feature, would I be able to log on to my router remotely and filter or unfilter his MAC address on those days when I am away on business? And if so, how would I access my router remotely?
Yes, that's exactly what its for.
You'll access the router from the internet using your external IP address and the port that is specified in your router settings.
If you are using a typical residential connection, you likely have a dynamic external IP that can change whenever.
For this reason, you will likely find a dynamic dns (DDNS) setting in there. If you set that up, you can use the dynamic dns domain name and the specified port to get to it from the outside