A beta reader is like a beta tester for software or apps - they get early access to your eBook to help you work out the kinks. Beta readers are incredibly valuable to indie authors. Not only do they offer fresh eyes to catch typos and formatting issues on a variety of different devices, but they also are often willing to provide input on things like character development and storyline. If your beta reader can't connect point A to point B, you can be sure the broader reading audience will have difficulty.
How to Find Beta Readers
The best place to start when seeking beta readers is your friends and family. You may have to instruct them that you're looking for honest feedback and don't just want pats on the back and a boost to your ego, but they are usually quite willing to help. Beyond friends and family, you may be able to reach out to your local library to help you find early test readers, and Goodreads has beta reading groups for most genres.
What to Expect from Beta Readers
The best way to know what to expect from beta readers is to provide them with some guidelines. Let them know that you're looking for constructive feedback. Ask them pointed questions about gaps in the story, flaws in the characters, flow of the chapters. Solicit their recommendations - you don't have to use them all, but they may help you improve your eBook.
Thank Your Early Readers
The best way to thank your early readers is with a copy of your eBook when it is published in final form. You can even give them an extra one to share with a friend so that they can help you spread the word about your eBook.
For more reading, K.M. Weiland has a great guide for beta readers
regarding proper reader etiquette.