Why when Swimming in water I feel that I run out of breath?

Because you can't breathe under water. And the same thing happens to me so I breathe more often when I'm doing my strokes and take breaks when I'm really out of breath. It means that you're not used to swimming certain distances and that you will soon get used to.

Another Answer:

Swimming is a very powerful cardiovascular exercise and gives your heart and lungs a very good workout. Because it is fun and we are not perspiring, we may not notice the workout we are getting. It may be just a sign of being out of shape...but any time anyone, regardless of age, feels like they have run out of breath during exercise, it is important to get a check up by your health care professional to be sure you are medically able to sustain that type of exercise or sport and to be sure that there is not some medical condition that you are not aware of under normal physical exertion, but which shows up when you are getting an especially good workout, like from swimming.