According to my 60D manual, the little light you refer to is most likely the "Access Lamp". Per page 33: "When the access lamp is lit or blinking, it indicates that the images are being written to or read by the card, being erased, or the data is being transferred."
I suspect this would most likely happen due to a slow memory card (less than class 10) when shooting RAW + Large JPG as I do, or, by extended noise-reduction processing for long exposures. I don't shoot video, but it might be lit while shooting video for the same reason.