I don't really believe in geniuses, but I believe in works of genius. Works of genius are at least potentially producable by a large proportion of the population, but not with any reliable frequency. Perhaps then a genius could be defined as one who is a prolific creator of works of genius.
Many of us have experienced that rare feeling of self-amazement of the result of the creative process. In could be in doing a drawing, composing a piece of music, proving a novel theorem, or writing software. When you create something, stand back and say; "how on earth did I do that?", "where did that come from?". That is a work of genius.