You're not actually extending the range of the wireless signal. You are "effectively" extending the range by adding a WAP (Wireless Access Point). WAPs are wired devices, that allow wireless devices to connect. These WAPs are also transparent to the network, meaning that they do not act as a router, but instead forward all packets to and from the devices they are connected to. As you can see on my network, I have 2 SSIDs and wireless devices can connect to either one and still use the DGL-4300 as the gateway, they don't even know (other than the SSID name) that they are connected to different hardware.
Your DGL-4300 provides 2 functions. #1 is a NAT Router. #2 is a Wireless Access Point (WAP).
Now, think of your wireless network as a sprinkler system for a lawn. You currently have your router, which is connected to the internet (using an ethernet cable). The sprinkler head (WAP) is right on top of your router and it sprays water out in a 50ft radius. Now, the lawn at 75 ft away is not getting wet. You need to connect a new water line (ethernet cable) to the router and run it out another 75ft, then connect another sprinkler head (another WAP) to the line. Now you have "effectively" extended your range of watering the lawn. You have not increased the water pressure, but you've placed another device that performs the same function as the first.
I hope this analogy helps.