Janmashtami is the yearly observance of Krishna's appearance on earth. It is one of the world's most widely observed spiritual festivals. Krishna's "birth," janma, occurred at midnight on ashtami, the eighth day after the full moon in the Vedic calendar.
Krishna's appearance is significant on many levels, and is something of a paradox. He's the beginningless Supreme Person, eternally existing everywhere at all times. He isn't "born" like we're are—forced by karma into a succession of material bodies. Krishna appears in His same permanent, spiritual form whenever and wherever He likes.
When He does appear, He chooses His devotees to play the roles of His father and mother. He Himself plays the role of their child, and acts like a human being, while also performing superhuman activities that are impossible for anyone else to imitate.