Is anyone in your family an avid reader? If they like books by foreign authors, it definitely pays to be able to buy from Amazon. The third book in a series I started has been out for a while in England but hadn't yet been released in America. But guess what! Some people in the US ordered the book from England and are now selling it on Amazon to other US readers who don't feel like waiting for it to show up in bookstores here.
Not sure if it'll work on your family, but if I didn't already buy stuff online on e-bay and other places, it'd be a pretty good incentive for me. Oh! And also out of print books. I got a book off e-bay that had been out of print for a pretty long time, so I wouldn't have been able to get it anywhere else.
Honestly, there are things that you just can't find in stores and for those it's great to have the ability to buy from e-bay, amazon, etc. I've gotten old movies that I couldn't find anywhere on the internet, video games that are for older systems (Nintendo 64, gameboy advance, etc.), opera libretti, and a bunch of memorabilia that I like to collect online. It's a great way to find things that you wouldn't be able to get your hands on otherwise.
Try explaining that it's nice because of all the things that you can't find in stores and have to rely on the internet for.