Most American libraries have agreements with Rakuten OverDrive (https://en.wikipedia.org/wiki/OverDrive,_Inc.) or something similar. OverDrive supports apps like Libby that let you borrow and read ebooks (and send them to your Kindle) that the library system has paid for licenses of. I have no information about the status of things like OverDrive, or Kindle support outside the US.

As for me, I rarely use Libby because most of the books I'm looking for do not have digital editions and even if they did no library would bother to pay for the license. (I miss having a research library handy.) In fact, I usually only use it for light audiobooks for road trips, but they usually have so long a waiting list as to make it useless.