BNR stands for Buy and Replace.
Someone sets up a treasury and usually lists guildlines in the treasury note. It gets sellers to buy from sellers, and you get noticed in the etsy community a good bit. So, they start out with 16 shops and someone buys from one of the shops listed and gets to put an item from their own shop in their place. buy and replace.
There are also ones called BNS- Buy and Stay
Pretty much the same concept as the BNR except when you buy from the first list of shops you get put on a waiting list for the next BNS which usually happens after the first BNS gets 15-16 sales since there are 16 slots for shops to be shown. BNS you have a better chance of getting multiple sales with only having to "buy in" once.