The simple act of working the soil gives a boost of oxygen that further stirs aerobic creatures to life. Soil is not dirt. Soil is a living microcosm populated mostly by good guys, and the garden is an ecosystem you can manage. Mostly good guys works out to be quite close to nearly all and managing that ecosystem requires careful thought about what you put into your soil. Think about earthworms.
Earthworms aerate the soil by channeling through it, thereby improving drainage.
They also add loads of worm-made castings that are great fertilizer. They also maintain good soil structure and control pests. You want to aim for a pH appropriate to growing vegetables, and a thriving population of beneficial organisms that break down organic matter into forms available to plants. . . Take a soil sample and send it to your state cooperative extension. Find out the pH and nutrient content.