In simple terms an organic fertilizer is made from organic matter such as bone, kelp or manure.
Chemical fertilizers are often made from petroleum or gasses from petroleum which are non-renewable resources.
When mixed with water, chemical fertilizers are usually in a form that a plant will use right away. It is very easy to over apply chemical fertilizers causing damage to the plants and creating runoff into our water resources. These fertilizers are also more easily removed from the root zone from too much water.
Organics are different. They are slow to be released into the soil and they are broken down into a plant useable form by bacteria and fungi. One advantage is that it is harder to over feed your plants since the soil micro-life breaks it down slowly. Another is that you can’t wash away a complete feeding because it isn’t readily soluble. Organic fertilizer tends to last longer in the soil so this slow and steady feeding tends to promote a healthy, more even plant growth rate. In general, organics are beneficial to the soil as well.
So to recap, organics tend to be better for plants, the soil, our water resources and in general better for people.
Hope that helps.