Peterr:
One other thing Trouble didn't mention is that the "N" standard and the very new "AC" standards greatly increase the distance the radio signal can connect to your wireless router from distance-wise. The "N" standard doubles and in some implementations quadruples the strength and therefore distance that your wireless device can connect to your wireless router from! On routers using the old "G" standard; you have a max distance of 70 meters (230 ft.) indoors; and with the "N" standard that is increased to 250 meters (820 ft.) for outdoors (like using your laptop on your patio or back deck). That's about 3-1/2 times the distance! Of course, these numbers are Maximums and can be affected by the building materials in your home, apartment, or office building and also the weather. If you divide all these numbers by 1/2 that is more likely the practical maximum distance 35 meters and 125 meters for most home environments.
What's really important with the "N" standard for you is that the ability of "N" to handle what we call auto-band-selection. This allows "N" based wireless devices to much more accurately sense and switch between bands at 2.4Ghz and 5.0Ghz at those greater distances--all the while employing the latest security encryption (WPA2) as Trouble mentioned. However, WPA2 wasn't really achievable using many "G" routers unless you used a high quality manufacturer such as Cisco-Linksys or Netgear. That meant spending more money, and most Consumers didn't really see the need to spend more for a "standard-device" like a wireless router, so they often bought whatever was cheapest at the local computer store.
The practical application of this is if you have other wireless devices in your home such as portable electronic home phones, they often use the 2.4Ghz bands; and the newest ones use 5.0Ghz. What that means to you is if you are using a "G" router that can't sense and auto-switch to the unused band, you will get dreaded and unwanted interference. This presents itself in random signal loss which is like a TV losing picture just when you don't want it to. The "N" does a much better job of avoiding this with the above built-in technology, and can do it at a much greater distance while keeping the ability to run the maximum signal encryption (WPA2). "G" routers or many of them suffer from distance limitation and have to "dumb-down" or select an older less secure encryption at distance option such as WEP.
That's a short tutorial on why you might want to go with the "N" router; it's like a "G" router on Steroids, and the new "AC" standard is like an "N" router on X-men quality steroids! Bigger, better, faster, more secure, more distance capability.
BIGBEARJEDI