The concept
BIN stands for Bank Identification Number, the first six to eight digits of the card. They indicate which institution issued the card, in what country, and whether it's credit, debit, prepaid, or corporate.
This is information available before the charge. You can use the BIN to display the correct currency, choose the processing route with the best chance of approval, or flag risk when the card's country doesn't match the country the buyer declared.
How it shows up in practice
You analyze your last hundred orders and find that many refusals come from a specific bank in a specific country. You put that bank's BIN on a different route, with alternative acquirer, and see approval rate for that segment go up. You start separating your routes by country and issuing bank, not by currency or buyer type.
Users spend most of their time on other sites. This means that users prefer your site to work the same way as all the other sites they already know.
The BIN, the first digits of the card, is information available before you charge. Using that info to choose the right acquirer, display local currency or flag risk when card country doesn't match buyer country, all of this becomes possible as soon as you can read the BIN.