Here are the basics:
The soil is alive!
It's full of microbes that do amazing things, like help plant roots receive more nutrients from the ground (see mycorrhiza fungi). Soil that is not alive with these microbes is called dirt. Soil grows food; dirt grows nothing. Soil stores carbon via this microbial life, and also purifies and stores water.
Also important to note: we also have living microbes in our bodies, mostly in our gut. In fact, we have 10:1 microbial DNA to human DNA in our bodies. Meditate on that when you realize:
When we spray chemical insecticides on soil, we kill these microbes. Food grown in insecticides and then eaten, keeps killing our good gut microbes once eaten. Food grown from unhealthy soil also contains less nutrition. It's possible to grow an orange with little to no Vitamin C!
Dead soil also does not store water and allows for polluted industrial and urban runoff.
Soil that dies releases carbon into the atmosphere, greatly exacerbating global warming. Healing our soil does the reverse: it sequesters carbon from the atmosphere.
We need to heal our soil in order to:
1) sequester large amounts of carbon from the atmosphere!
2) store and purify water!
3) restore nutrients to the food we grow and eat!
We heal our soil by composting organic matter, and by repopulating microbial populations with soil amendments.