There are many reasons for this. Exercising muscles need energy, and they get that some of that energy from blood glucose. As the animal exercises, the blood glucose decreases. Exercise also increases the heart rate and increases the blood circulation. The increased blood circulation causes insulin to be absorbed more quickly, which causes the blood glucose to drop.
Exercise can dramatically increase the rate at which insulin is absorbed.
You would be surprised at what small changes in activity can do. What you think is a relatively low level of activity may be enough to seriously lower your pet's bg. Here are two personal experiences from owners whose diabetic dogs became seriously hypoglycemic because of a change in the daily activity routine. So today I took her with me to a dog show. She used to be a show dog, so I thought she would enjoy going with me.