There's two different things to think about when we talk about Food Production. One is domestic food production (usually covering home vege gardening and having chickens for eggs or meat) and the other is commercial food production.
Food production can result in tremendous negative effects on the environment, especially in commercial situations where water is redirected from natural sources to irrigate, pesticides and herbicides are used to control unwanted insects and plants and artificial fertilisers are used to promote growth beyond what the land can naturally support. Food then has to be transported. Some animal products (like eggs) are produced in a really unethical way. These advances in growing technologies and agricultural techniques have drastically improved the crop and meat yields over time, but many aren't sustainable. Some of the effects are: