I believe that JG would probably have been referring to 1. users who don't leave Bitcoin always running (only starting it to send money), and 2. users with firewall-blocked incoming connections.
The Bitcoin software itself is a p2p node when it is open. Bitcoin allows incoming connections from other Bitcoin clients on the Internet, and these connections can receive and relay information about transactions and the blockchain to other clients. Good connectivity ensures that others are able to receive the blockchain quickly, and that transactions are quickly relayed.
When Bitcoin is run for the first time, it doesn't know about any other Bitcoin client IP addresses, so it connects to irc.lfnet.org (an IRC chat network with multiple servers) and listens to the #bitcoin channel for the IP addresses of other users. Previously found IP addresses are then cached in the addr.dat file for faster startup in the future and for sharing with other clients. Bitcoin then connects to other p2p clients to begin downloading the past 140,000 or so Bitcoin transaction blocks. There is a backup plan, where IP addresses can be manually added to the configuration file if a user can't make the IRC connection.
However, if the inbound TCP port 8333 is blocked by a firewall or NAT box, clients won't be able to connect to you, and your Bitcoin will be limited to just 8 outbound connections (instead of 125 bidirectional connections) Therefore, port 8333 in gateways/routers/firewalls/whatever you call that Netgear box should be port-forwarded to the internal computer running Bitcoin, and provisions should be made to assure the internal computer gets a static IP assigned through DHCP or manually.
Bitcoin miners are doing something different - they are ensuring that the Bitcoin transaction blockchain is cryptographically secure. Since most are pool mining, they don't need to have the Bitcoin client open to do this.
So, although you aren't making bitcoins from doing it, leaving bitcoin software open and ensuring that it is able to make many connections to others helps all Bitcoin users.