Quality of the flash, and the ISO level of the camera. Many family get together's occur at night, in poor lighting, like dinner at a restaurant, or a wedding reception, or Christmas dinner around the dining table. A camera that deals with that well will take better pictures of the events you want to capture. Also the quality of the anti-shake technology, which again will help dealing with low light conditions. Don't let anyone talk you into some fancy DLSR, or some other camera with a zillion bells and whistles. You want a convenient camera that can take a good picture at a party. It's not the same thing as sports photography or portraiture. Anti-shake, good flash, with good performance in low light levels (good ISO). That's what you want.
Technically we are talking about the maximum f-stop of the camera, or it's "speed", but for the $200 price range that's not going to be easy to assess, and many other factors (like anti-shake) also impact the camera's ability to deal with poor lighting conditions.
Probably also worth checking out how quickly the autofocus works under poor lighting conditions. Auto-focus can get messed up by low light too, you want something that takes a good picture quickly.
