What is making the veins in my arms and legs to stick out so much?

Multiple reasons. Veins return blood back to the heart and can carry a large volume of blood. Depending on many factors including levels of hydration, genetics, outside temperature and even physical activity, the size of the veins will vary. Another important function of the veins is to help control body temperature and this too will affect vein size. Also with aging, veins enlarge as tissue volume decreases.
Circulation problem. Dilated veins in your lower extremities is a sign of a circulation problem. You need to get checked out by your doc to find out what is causing this problem.