If you've ever changed the station on an AM radio at night, chances are that you would have picked up some radio stations from other cities while turning the dial. This is what medium wave DXing is all about - picking up AM stations from other cities and countries and keeping a log of them.
The first time I remember picking up a radio station from another city was when I was at my grandparents' house on the hill in Sumner, Christchurch, back in the 1980s. I was playing with their radio - one of those big old radios that were built solidly and lasted forever - and picked up Radio Windy from Wellington.
I now have a Sangean ATS-505 radio. As well as picking up stations from around New Zealand (mainly Newstalk ZB and National Radio), I have picked up stations from the east coast of Australia. The ABC's stations come in clearly, but I have also managed to pick up local stations such as 2WEB from Bourke, NSW. And to show how peculiar medium wave DXing can get at times, I have managed to pick up 2GB in Sydney, despite the fact that Newstalk ZB broadcasts on the same frequency in Ashburton, which is just down the road. I have also received 4BC from Brisbane which broadcasts on the same frequency as National Radio in Nelson.