By the end of the first trimester it's normal to begin feeling a little breathless. This is because your heart and lungs are having to work much harder to supply your body with oxygen due to all the changes that are taking place to allow the baby to grow.
The amount of oxygen you need in pregnancy is about 20 percent more than normal; some of this goes to the placenta (see You are 10 Weeks Exactly) and baby and the rest to your other organs. To get this increased amount of oxygen you breathe faster and deeper, almost hyperventilating so you feel short of breath, especially when you exercise.
As your pregnancy continues, you may find that this shortness of breath or feeling that you are not breathing very deeply continues, or worsens. As the baby grows, your uterus will expand upward and your other abdominal organs will rearrange themselves to create more room. Your organs and uterus push up against your diaphragm so it becomes more difficult to take a deep breath, so in order to get all the oxygen you need, you then have to breathe much faster. The hormone progesterone may also affect the rate at which you breathe.
If you have any concerns about breathlessness, don't hesitate to speak to your doctor.