All lenses have 2 basic details - how much light they let into the sensor and how much stuff they can fit into the photo. When we look at phone cameras, since they are fixed and irreplaceable it's a good idea to check these before buying the camera. For example modern phones such as the Samsung Galaxy S6, LG G4 and iPhone 6 have lenses rated at "f2.0" or "f1.8". The lower this number is, means that their lens is able to squeeze every last drop of light available - so if you compare to an "f5.6" lens, this larger number means that the lens is not ideal to take pics in dark environments - so the camera will be forced to use the flash all the time
Aperture also effects how the picture looks - unfortunately many mobiles and pocket cameras today do not allow the user to set this manually. Either way if you want to check out the effect of varying the f-stop on the image, check out this YouTube Video
The Bobble-Head Effect
Camera/Phone lenses build their image based on how far they are from the subject. Now this is all well and good when you are taking a nice landscape with your phone, however since most phones use wide angle lenses to be more versatile they are very easy to misuse when shooting subjects close up (like people!). For example - you want to take a nice portrait using your phone.. and as you walk up to the person and fill the frame with their image, you start to wonder why your friend is somehow looking like Gollum.
The reason is that since you are now much closer to your subject, the distance between the lens and their nose and the lens and their ears is proportionally very different. What's going to happen here? since the nose is closer it will look bigger, and since the ears are far away they will look smaller or be completely hidden by the cheekbones. Big nose + no ears makes for a bad pic.
To fix this, we're going to rely on the fact that most phones nowadays have 8/13 or even 20 Megapixel cameras. That's a LOT of detail - keep in mind that Full HD equates to around 2 Megapixels. So the easiest way to get the shot is to take a couple of steps back, compose your photo leaving some extra around the subjects, and then simply crop the image using any number of simple applications.