Does anyone know if you can download ebooks from the library onto a Kindle?

My grandma got a Kindle for Christmas. She has low vision and wanted to be able to read more. My mom asked me what she should get her and I told Mom to get a Kindle. I didn’t know much about them or do much research, I had just heard the name. Well, after I was put in charge of purchasing and loading the books on the Kindle, I fell in love with it. I did more research and bought myself a nook on Friday. I like it better because I can lend books, buy books from other sites, etc.

Our local library offers ebooks. Is there any hope for my Grandma and her Kindle? Or should we put the damn thing on Craigslist and buy her a nook?