There are several benefits to using compost in your organic garden.
For one thing, the decomposing vegetable matter provides plant nutrients -- the very sorts of nutrients that become depleted in the soil when you harvest your crops!
Another benefit is mulching -- adding compost on the surface of the ground around the base of your garden plants. That helps shade the ground so the moisture doesn't evaporate so quickly, and also reduces the likelihood of erosion.
In addition, incorporating the humus of compost into your soil helps it hold water more effectively, helps keep the soil friable, and aids both drainage and aeration. It encourages the activity of earthworms, too, which provide natural fertilizer in the form of their "castings."