It means that a book has been - for any length of time - on the New York Time's Best Seller's List. This list aggregates sales data from thousands of venues in the United States for several different genres of books. It gathers data weekly and the data is published two weeks after data gathering (so the November 28 print edition contains the November 14th data).
Being a New York Times best seller is not necessarily an index of quality. It is an index of "hotness." A book is moving fast to make it onto that list. The idea behind advertising it is to help the book pick up even more steam. If a book spends several weeks on the list, this is an indication of a book that sells extremely well.
The reason that it seems like this encompasses so many books is that you hear about books that are NYT best sellers because they are being purchased, read, and talked about. The reality is that this list contains fewer books than you would think.