If I gave my story to someone to read, I would want them to check for spelling and grammar, check for continuity issues, check for blatant mistakes and plot holes and tell me if there is anything that they particularly liked or disliked. Spelling and grammar I would fix. Anything else I would examine and determine if it was really a mistake or if I knew something that the reader didn't. As far as what they liked and didn't like, if one person told me, I might ignore it. If everyone that read it told me that they didn't like a scene, I might look it over and see how I could change it. What you need from a beta reader would partly depend on what you are writing. If you're writing hard Sci Fi you might want someone who could check your science. If your righting military fiction you might want someone with some knowledge of history and/or of weaponry.