Come on is a fast phrase which is meant to [persuade] someone into understanding a different perspective.
It can be used to attempt to help someone agree/convince them that you have their [best intentions] in mind.
Come on can also mean that somebody is being too slow, and they need to do something faster.
Come on isnt meant to be used literally.
However, the phrase is common, yet vague, [nondescript], and should not be used.