When your pulse speeds up, it's an obvious indicator that your heart is working overtime. Your pulse reflects your heart's pumping speed: Each beat of your heart pushes blood through your body, and you can feel the pressure of each push in places like your wrist or your neck.
When your pulse rate increases, it means your heart is pumping faster. It can also mean it's having trouble pumping and is working harder and faster to get enough blood to your body parts. This can mean you're having a heart attack.
The trouble is, an increased heart rate, even in combination with shortness of breath, could also indicate other things -- especially if you're exercising. A good way to tell if your heartbeat is speedy because you're running or because you're having a heart attack is to sit down and see if it slows down. If it doesn't, and you smoke or have high blood pressure or high cholesterol, and especially if you also have pain in your left shoulder or arms, get to a phone and worry about sorting it out later.
To complicate matters further, a racing heart and shortness of breath can also be a sign of an anxiety attack, and a feeling of anxiety is also an indicator of a heart attack.