Q: What does it mean to “enable the wireless router radio”?
A: The wireless radio is the device inside the wireless router that sends out the wireless signal. Turning it on means that you are enabling the router’s ability to send out a wireless signal. If you have a wirless router and you don’t want to use it for wireless (e.g. you only want WIRED access for now), you can turn off the wireless radio (which is the same thing as saying that you are “turning off the wirless”).
Don’t confuse the radio on/off with the SSID broadcast on/off. Each router has a name (the default is linksys for a linksys router and you should change it) and this name is the SSID. You can elect to turn this SSID broadcast on or off. With the broadcast on, then computers in range will have an easier time finding your router than if the broadcast is off. But to make it clear, if the radio is ON (e.g. the wireless signal is available), you can have the SSID on OR off. Personally I keep the SSID on when I’m setting up a machine to access the wireless router, and I turn off the broadcast when I’m done.
You can read this article for a good checklist and guide to linksys router security.