Why compost for my garden?

If you were to walk out into the woods, brush the leaves away from the ground and take a good look at the soil, what would you see? You would see natural, rich, healthy soil that is perfect for growth. The leaves and twigs fall from the trees, lay around for a while on the ground, and eventually breakdown for the new plants to grow in. This is a perfect medium for healthy plants. Compost is the same thing, except we can customize it and speed up the process depending on our soil needs. We rake up our leaves and throw them into a pile along with food scraps and whatever else we may have. We water the pile and mix it up so that it breaks down quicker. We can add things like seaweed, wood ash, oyster shells, or anything else we may need to make the soil we have into the soil we want to have. 
This broken down organic matter does many things for our plants. It provides essential nutrients like nitrogen, phosphorus, potassium, calcium, sulfur and micronutrients that plants need to grow. It adds texture to the soil so that there can be adequate air exchange and water retaining and draining abilities. It is much less compact and dense than standard dirt allowing for roots to move around more effectively. The composting process causes the soil to heat up and therefore kill pathogens and some weed seeds. Compost laid out in your garden can also prevent weeds from coming up and prevent erosion similar to how mulch works. Is that enough reason for you yet?

New sprouts in compost