Primary Listing
  
You have your main house where you live most of the time. You also have a summer cabin down by the lake, where you spend a lot of time between the beginning of June and the end of August. In addition, you’ve got a timeshare in Colorado, where you spend a couple of weeks every winter. And you spend every Easter at your sister's place in Florida. You spend a lot of time moving around. But your primary residence is still the main house.
A primary listing works like that, only for publicly traded stocks. It represents the main stock exchange where shares of a particular company trade. It may be listed on multiple exchanges (both the London exchange and the NYSE). But one of those represent the primary listing.