The depiction of Lord Krishna in blue colour has been there since time immemorial. Even in many ancient paintings thousands of years ago Lord Krishna can be seen depicted in blue. Lord Krishna is the incarnation of Lord Vishnu and his blue colour depicts internal strength, calmness and serenity therefore lord Krishna has blue skin. Lord Vishnu’s symbolic representation is water and in nature the rivers, lakes & oceans are all depicted in blue.
When Lord Krishna was a baby, Demon Putana fed Krishna poisoned milk to kill him. But, Krishna did not die, instead his skin turned blue.
Another one goes like this….
Many people also believe that the entire cosmic
strength resides inside Krishna which is not visible to
normal human beings and hence Krishna appears blue.
Its believed that Krishna had to fight injustice in the
society at every stage of his life. It resulted in his body
taking blue colour for absorbing the sins of the society.