Plantar Fasciitis is one of the most common causes of heel pain in runners.

It involves pain and inflammation of a thick band of tissue, called the Plantar Fascia, which runs across the bottom of your foot — connecting your heel bone to your toes. Plantar Fasciitis causes stabbing pain that usually occurs with your very first steps in the morning. Once your foot limbers up, the pain of plantar fasciitis normally decreases, but it may return after long periods of standing, getting up from a seated position, or running/walking.     

*Below is not a diagnosis of your condition, and its sole use is for reference material on common issues of Plantar Fasciitis. This does not include all details, causes and treatment options for the condition.
The main physical causes of this condition are:

Tight calves will increase tension on the Plantar Fascia.
Altered foot function: Excessively flat or high arches.
Lack of big toe extension- Upward movement of the big toe.
Tight hip flexors will reduce the ability to use Gluteals in ‘push off.’
the phase of the stride, hence increasing the work load on the Plantar
Fascia and calves. {2}
Reduced glute and hamstring strength will again increase the demand on the calves and Plantar Fascia, predisposing to an overload of these structures.
                Other non-biomechanical reasons for the condition can be improper running technique, worn-out or improper running shoes, and increasing mileage too fast. If you feel any of these, or other non-biomechanical reasons may be an issue, please confer a reputable running coach.  
                From a physical standpoint, the best way to prevent Plantar Fasciitis is to obviously correct the causes by performing stretches and exercises to correct any of the above dysfunction.  Stretching for the Gastrocnemius (upper calf), Soleus (lower calf), hip flexors (See picture below), and the Plantar Fascia (See picture below).  Secondly, you need to be evaluated to determine if you have excessively flat or excessively high arches. If you have flat feet, an orthotic may be beneficial. With high arches, manual therapy can help reduce the rigidity and tightness of the foot/arch. Lastly, strengthening of the glutes and hamstrings (along with hamstring flexibility) are vital to proper push-off mechanics during running.