What it means
Firefox's local-network prompt asks whether a particular website can connect to devices or services on the user's local network. A router firewall and device firewall govern broader network traffic. Allowing a web page is not equivalent to opening an inbound router port from the internet.
A real-world example
A casting site asks to find a living-room TV. A user allows that site for the session, but has not changed the router's public-facing firewall settings.
What to do
Check the requesting domain and intended device before allowing. Remove persistent grants when finished, and manage router and device exposure separately through their own settings.
The distinction that matters
The prompt does not certify a website as trustworthy, and a Deny choice does not patch vulnerable smart-home firmware. It is an extra browser boundary that can prevent an untrusted page from interacting with reachable local services. Keep that distinction clear during troubleshooting.
Mozilla's local-network boundary