First lets get the color straight. He’s not “blue.” He is śyāma / nīla.
The color śyāma is “Dark (black), with slight blue-green coloration.” A really heavy monsoon cloud, for example, is śyāma. The color nīla is “Dark, black, bluish/greenish-black.” A sapphire (nīla-maṇi) is a common example of this color.
So, basically, Krishna is black with a sapphire-blue luster.
OK, now let’s get to the “why” part.
Why is Krishna black? Why is anything black? What is black? Black is what you see when an object reflects no light. Black things absorb all the light that falls on them, letting nothing go. When something attracts all the light, and nothing escapes, it’s black.
And that’s why Krishna is black, because that’s what Krishna is – All-Attractive.
Throughout the Veda, “light” is used to describe consciousness, because consciousness illuminates existence. Our consciousness can shine its light anywhere. When it shines on something beautiful, it get’s stuck there. We’ve all experienced a song we can’t get out of our head. A girl or boy we can’t stop thinking of. A sunset we can’t take our eyes off. A game we can’t stop playing. Attractive, beautiful, delightful things are “sticky”, sticky with light, sticky with consciousness. They are “black.”
Krishna is so black, because he is All-Attractive. When our consciousness falls upon him, it sticks there forever. When light falls upon him, it never bounces off again. He is black. He is so fascinating, so delectably sweet, so delightfully deep, so thrillingly pleasurable, so enthrallingly enchanting and adventurous… no “light” escapes.