The concept
Global checkout is the checkout page built to serve buyers from more than one country, automatically adapting the displayed language, the currency shown to the buyer, and the payment methods available according to the visitor's origin.
A checkout that doesn't recognize the buyer's country and always shows the same language and the same currency tends to convert less: part of the abandonment in international sales happens because the buyer doesn't understand exactly how much they'll pay in their own currency.
How it shows up in practice
You sell to Germany, Mexico and Brazil at the same time. A Mexican buyer reaches your checkout page and sees everything in Portuguese and US dollars. He doesn't know exactly how much he'll pay in his own currency, doesn't understand the page, abandons the purchase. You build a global checkout that identifies visitor country, changes language and currency automatically, offers his local payment method.
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.
When each visitor sees their own language and currency without effort, abandonment rate drops significantly. Global checkout isn't an extra, it's the difference between an international operation that works and one that leaves money on the table through simple misunderstanding that currency and language change buying decisions.