The most important characteristics of a camera are the resolution (measured in megapixels), lens focus type (either fixed or automatic) and the presence of a flash. The flash could be either LED (single or even double) or xenon.
The number of megapixels is not always a good measurement of the quality of the photos, but if you plan to print pictures, you would generally get higher quality ones out of higher megapixel cameras.
Auto focus lens are not a guarantee of better image quality, but fixed focus cameras are usually inferior. Most importantly, only auto focus cameras can allow shooting of really close objects – i.e. macro shooting.
Some phones offer optical zoom but those are rare. Most use digital zoom, which degrades the quality of the photo.
Cameras that can work in “video mode” are characterized by the maximum resolution and framerate (frames per second or fps) of the recorded video.