Just as a mom can distinguish coos and smiles, it's not long before a new mom can distinguish between cries - whether it's sad or angry or something else.
From the moment you meet your baby, you realize that he is a true individual with his own likes and dislikes. Of course this was absolutely true with my son. While he rarely fussed, I knew how to distinguish his needs within a few days of being his mom. He had a specific cry for certain things. If he was hungry, I knew. If he was wet, I could tell too. It's amazing how easily connected you can become to your baby's own communication style - no matter how simple it might be.
Crying is of course normal, but it doesn't mean that it is any less frustrating. For parents, it alerts us to a problem. For babies, it's the only way they have to communicate! And there are times when we really have no idea what is wrong. It could be colic, or gas, or scared or even angry. There's a multitude of reasons. But as the days go on, it becomes easier and easier to find the reason for the cries.