Many Hindu gods and goddesses are depicted with blue skin. This does not necessarily mean that Krishna--or other blue-skinned divinities such as Shiva and Rama--actually had blue skin. As Sadhguru explains, it is possible that Krishna was dark-skinned, but "people who were aware saw the blueness of his energy, so they described him as blue." This blue energy field--commonly referred to as an aura--is what artists tend to emphasize when they depict Krisha.
This blue aura represents the "all-inclusiveness" of Krishna. Additionally, the blue aura represents his irresistible attractiveness (this is different than attractiveness derived from mere physical traits) . Sadhguru gives one striking example of Krishna's ability to attract even people who hated him.
He was so irresistible that even Poothana, the assassin who came to kill him when he was just a baby, fell in love with him. She was with him for just a few minutes but she became completely entangled in his blue magic.
As this example represents, Krishna's aura endeared people to him. Thus it should be unsurprising that one of his most memorable traits was his blue aura or or energy field.