​Amazon Ranking

That is complex. It depends on how well the book performs in terms of sales and the book category.
Today, I’ll talk about regular rankings, that is, all-time to date for book performance.
My book is a memoir and history.
Everyone can check a book sales performance (if there are enough sales for Amazon to build statistics). On the page where you can buy the book, scroll down the page, and you may see something like this (Canadian Amazon site): see below. 

The Amazon algorithm considers the number of copies sold, how recently, and the sales amount. I think the rank jumps significantly after some good sales. I remember on “Amazon.ca,” I was #1 one day after just 3 sales on the Canadian Amazon site, one eBook and two prints. It was in the “Romanian History” section. Not many buy books in Canada about someone’s memoirs in Communist Romania. But still, a few days later, with no more sales,  I was #28 in the same category.

​On the American site, I was #71 in Romanian History with 436 sales (419 eBook and 17 print)
Americans seem to be more interested in European history than Canadians, even considering they are 8-9 times more people.

 
I have also attached the book on performance in the UK. It seems they are the most avid readers of the history of Romania, considering how many history books were ahead of mine (I was not on the list for Romanian history), and I had similar sales in the UK to those in Canada.

​Conclusion: if someone said they were #1 on Amazon, you should ask them the category at least. If they said it was #1 in romance (for example), it means a lot, while in a category with fewer readers, high positions could be reached fast.
Another remark: looking at rankings for many books, I observed that readers enjoy more books about sex than philosophy, history, and politics. Uffff.