In running, you have to overcome the force of gravity and friction while staying balanced. If you get tired and apply less force you will slow down with each step because every step is alters how fast you are traveling while in the air. This is why running downhill is easier, the ground is naturally slanted downwards so you don't have to use as much energy to push up. On the other-hand, a uphill run requires much more energy because in order to travel the same amount of horizontal distance their is a larger vertical distance to overcome.
If it is a sunny day, your shoes will mostly have static friction while running. However on a rainy day, your shoes will be covered in mud and will grip the ground less efficiently. You will probably slip and experience kinetic friction unless you wear very good spikes and watch where you run!