Buying anything which has a lot of choices and the details are buried under multiple technical jargon's is a difficult proposition. It becomes more difficult with the number of choices in market. The world is though ruled by couple of big names but there are many small players who either offer very good quality or features packed at attractive prices. And then there are many sites whose sole job is to compare the different features. What we will do here is to demystify the various elements of a smartphone to make sense of them.
Display size tells about how big or small is the screen. Display size is usually given in inches and there is a single number and not length and breadth as we are used to when we look into an area. The
display size given is the diagonal length of the mobile screen. But if you really see what we as a buyer concern about is the area of usage and the diagonal length can be misleading at time. How much you thing a 6" display size will be bigger than 4". Twice? See the picture below and judge yourself
Though the diagonal size is just 1.5 times the area is more than double. If you eat pizza, then apply the same logic to your 6" and 10" pizza. The bottom line is that have an eye on area.
The story does not ends here. There is another thing to consider of, which is aspect ratio. The same diagonal can result in different aspect ratio and hence different area. What is an aspect ratio? Aspect ratio is the ratio of length and breadth. Look at the following diagram and it will be clear. The circle is of diameter 7" so you can fit many shapes there.
With the above understanding hopefully will give you important understanding about the display sizes.
The other term to look around is the resolution. You will see a number like 1280 x 780 pixel. What does that means. Each pixel is like a dot on the display screen. Computers don't render by long brushes. The build an image by painting each dot on the screen. And when we say 1280 x 780 pixel that means there are 1280 dots along length and 780 along width. So the higher the pixels the quality of image would be higher. Also the high quality image when zoomed will not pixlate however with low resolution images, they will pixlate at higher zooms. See the image below and note the serrations at 500 x 500 pixels of a 100 x 100 pixels image
Then there is million of colours. It tells about the device capability to render the variations of all types of colour. Normally you will see 16 million colours and I would not worry about much beyond this. Some device might say trillions of colour but I would worry about that only if I am Picasso or Michelangelo