It could be to reduce camera shake. I use this technique in a lot and in poor light it can be very effective. Pushing the shutter button causes the camera move a little, so by holding it down for a burst of three, the first image may have some residual movement from your finger, whilst the last image might have some shake as you start to release the shutter, but the middle image is usually ok.

Additionally, as camera shake is a random motion simply by shooting more images you are more likely to have a sharp image.

Other explanations might be to do with unanticipated motion, capturing the best facial expression. Another way of looking at this question is by asking what are the disadvantages of shooting in burst mode?. Other than battery/memory card usage there aren't many. Shutters still have a limited life but that's extending into the hundreds of thousands of actuations these days. Compared to shooting film with the cost of developing and frequency of changing rolls, taking a photo with digital is about as close to free as it gets.