A wireless access point has an Ethernet port, through which it attaches to the fixed (wired) Ethernet. It bridges wireless signals in range - passing frames to and from those devices and devices attached to its Ethernet port.
So yes, it needs wiring in to one of your modem/router's Ethernet ports; and therefore you may find it just as easy to move the box you have - which AsIUnderstandIt has both an ADSL port for your phone line and wireless capability (and I'm guessing one or more wired Ethernet ports too). If you're just experimenting with a better location for it, you can run a gert big long RJ11 extension - they're cheap as chips - while shifting the Belkin about the place, and worry about neatening up the cable route once you know it's worth putting the ADSL-wireless box halfway up the lounge wall, above the kitchen cupboard, or wherever. (Since the ADSL signal's travelled several - mayhap tens - of thousands of feet between the exchange and your house, an extra 50 foot of extension cable isn't going to make a massive difference...)