Why - because you don't need equipment and it is a simple but great way to increase your shoulder, chest, and core strength.
How to do More
Benchmarks - I know an 80-year-old man who does twenty pushups per day in addition to planks, situps, and squats. He is stronger than most men in their 60's.
Start where you have to start even if it's half pushups from your knees and get to where you can do one or more real pushups. Then work on increasing the number daily until you can do thirty or even twenty and do multiple sets of twenty. Once you reach twenty you can always finish it with ten more half pushups.