What is fertilizer and why do plants need it?

In order for a plant to grow and thrive, it needs a number of different chemical elements. The most important are:

• Carbon, hydrogen and oxygen - Available from air and water and therefore in plentiful supply
• Nitrogen, phosphorus, potassium (a.k.a. potash) - The three macronutrients and the three elements you find in most packaged fertilizers
• Sulfur, calcium, and magnesium - Secondary nutrients
• Boron, cobalt, copper, iron, manganese, molybdenum and zinc - Micronutrients

The most important of these (the ones that are needed in the largest quantity by a plant) are nitrogen, phosphorus and potassium. If you have read the articles How Cells Work and How Food Works, you have heard about things like amino acids, cell membranes and ATP. Nitrogen, phosphorus and potassium are important because they are necessary for these basic building blocks. For example:

• Every amino acid contains nitrogen.
• Every molecule making up every cell's membrane contains phosphorous (the membrane molecules are called phospholipids), and so does every molecule of ATP (the main energy source of all cells).
• Potassium makes up 1 percent to 2 percent of the weight of any plant and, as an ion in cells, is essential to metabolism.

Without nitrogen, phosphorus and potassium, the plant simply cannot grow because it cannot make the pieces it needs. It's like a car factory running out of steel or a road crew running out of asphalt.
If any of the macronutrients are missing or hard to obtain from the soil, this will limit the growth rate for the plant. In nature, the nitrogen, phosphorous and potassium often come from the decay of plants that have died. In the case of nitrogen, the recycling of nitrogen from dead to living plants is often the only source of nitrogen in the soil.
To make plants grow faster, what you need to do is supply the elements that the plants need in readily available forms. That is the goal of fertilizer. Most fertilizers supply just nitrogen, phosphorus and potassium because the other chemicals are needed in much lower quantities and are generally available in most soils. Nitrogen, phosphorus and potassium availability is the big limit to growth.
The numbers on a bag of fertilizer tell you the percentages of available nitrogen, phosphorus and potassium found in the bag. So 12-8-10 fertilizer has 12-percent nitrogen, 8-percent phosphorous and 10-percent potassium. In a 100-pound bag, therefore, 12 pounds is nitrogen, 8 pounds is phosphorous and 10 pounds is potassium. The other 70 pounds is known as ballast and has no value to the plants.
So why don't people need fertilizer to grow? Because we get everything we need from the plants we eat or from the meat of animals that ate plants. Plants are factories that do all of the work to process the basic elements of life and make them available to us.