Benefits to Plants
Like chemical fertilizers, organic fertilizers provide the nutrients plants need to grow. However, with organic fertilizers, those nutrients are released more slowly, eliminating the possibility of overfeeding.
Organic fertilizers must be broken down by soil microorganisms before they can be used by plants. Because of this, nutrients stay in the soil longer instead of being washed away by heavy rains. You don't have to apply organic fertilizers as often as you may chemical fertilizers because of this, and the absorption of nutrients is spread out over time as the plant needs it.
Another benefit of the breaking down process of organic fertilizers is, it creates stronger plants. By design, plants are supposed to break down nutrients to make them usable in much the same way that you need to chew your food to be able to swallow and digest it. Take that away from a plant and its ability to break down what it needs begins to diminish, creating a weak plant.
As already mentioned, you shouldn't need to apply organic fertilizer as often as chemical fertilizers. That alone is a cost savings. Also to be considered is that fact that many people can make their own organic fertilizer using compost, manure and other items that can be found easily.
Often when you apply chemical fertilizers to your lawn, you are advised to keep pets and children off the lawn for a certain period of time. That's because these chemicals are poisonous and can be harmful if they are ingested. This is not a worry with organic fertilizers. And as a bonus, the wildlife, which isn't likely to stay off the lawn after fertilizer is applied, won't be harmed either.
Benefits to the Soil
Microbes that thrive in healthy soil can be killed when chemicals are added. This is because chemical fertilizers are only intended to provide specific nutrients that make plants grow, so the soil may become acidic when it gets unbalanced. Eventually, the soil just isn't fertile anymore and becomes dead.
Organic fertilizers feed the soil, allowing microorganism and worms to flourish. Worms and other creatures in the soil provide their own fertilizer and also help keep soil aerated, which is essential for plant growth.
Healthy soil is alive and sustainable for as long as organic amendments are added. This means vital nutrients are always available for the plants you want to grow.
Benefits to the Environment
Even when carefully applied, chemical fertilizers can run off and contaminate our water sources. These chemicals do not break down so they can do damage for a long time. Organic fertilizers are almost always biodegradable, so even if they run off into waterways, they won't usually do any harm.
This is not to say that organic fertilizers can't do any damage. That isn't the case. Fertilizers that have not been broken down properly can still contaminate waterways. If used incorrectly, some can even hurt plants. So whatever type of fertilizers you choose, make sure to follow package directions and use them correctly for the biggest benefit to your garden and the least impact on the environment.