Consider all of the wireless gear you have operating at your home. What wireless does your current wireless router support? Wireless-N? Wireless-B/G? Wireless-A?
A dual band router, in a nutshell, gives you two radios instead of one. In a standard single band router you might configure and support Wireless-N or Wireless-A. With a dual band router you can now dedicate a radio to Wireless-N and the other to Wireless-A. Some of these radios will only operate one of the radios at a time. In this instance you get wireless-N or wireless-A but not both.
Other dual band radios are capable of running both radios simultaneously, In this case you could run both Wireless-N and Wireless-A at the same time.
In terms of specific recommendations, I'd recommend considering the Cisco Valet routers. They're a step up from the Linksys routers and a supported by Cisco,
