I'm not sure if we are the only species who cry or what the evolutionary advantage of it is, but personally I think we always feel better after a good cry because it is an outlet or a way of expressing pent up emotions that may otherwise become suppressed and part of the baggage we sometimes carry around.

When we are happy, we like to express it. When we are sad or grieving, tears can be a way of expressing the intensity of that emotion in a healthy way and letting go so we can move on. Emotions need to be expressed and tears are a wonderful part of the healing process.