The semi-short reason why is:
The plantar fascia is a sheath of tissue that starts in the base of the heel and continues forward across the sole of the foot and attaches to the bones in the front of your foot. It stretches and lengthens when you stand, and shortens when your foot is in a relaxed position (when you are sleeping) PF strikes when the tissue stretches beyong its normal limits. When Achilles tendon or calf muscles are tight, the soft tissue of the plantar fascia stretches too far. It gets tiny tears, which become irritated and inflamed. When you go to sleep the tissue retracts as the foot relaxes to its nartural position. Then, when you wake and put your weight on it as you step out of bed, the fascia gets a sharp or sudden tug as your arch flattens, irritating the injured tissues again.
Thats why the pain subsides when you walk and/or stretch your calf muscles - you are gradually stretching the tissue again.
Hope that makes sense!