I live in the country. My septic field is under a hill in the yard. How does this type of system work?

This sounds to me to be a mound system. Most of the time our septic fields are placed in the ground but sometimes the ground in our yards is not suitable for draining away the water in our waste water system. Most of the time this is because the water table is too high or the soil is just not very good at absorbing the effluent. This is when a mound system is usually used. In the mound you have a series of pipes that become pressurized when the pump kicks in. The mound is comprised of sand and gravel what does the work of the normal absorption field. If you have a mound check the toe or the end of the mound for a breach on the earth by the water in the mound. Often if the mound is saturated it will begin to wash out the toe.