There are a couple of things that cause the camera to be "busy." As JR60004 mentioned, it could be because your buffer is full. When you take a picture, the camera puts the picture into a memory buffer and then writes from there onto your memory card. If you take a lot of shots quickly, the memory buffer can fill up and the camera won't let you shoot again until it has written some of those pictures to your memory card.
Another possibility, if you were taking very long exposures, is that your camera was doing dark frame noise reduction. When the camera is set to do noise reduction, it doubles the amount of time it takes for each picture. If, for example, you were taking a 4" fireworks exposure, the camera would keep the shutter open for 4" to record the picture. It would then record a blank image with the shutter closed for four seconds. The camera would use information from the second (blank) exposure to help eliminate noise in the first exposure. That makes for lower noise pictures, but it significantly reduces your picture taking speed. I leave noise reduction on when I'm shooting long exposures of things that won't be going away, but for things like fireworks, I turn it off.
