Ben,
Yikes!
Every fertilizer comes with a guaranteed analysis on the package (or it is not a fertilizer like Superthrive to JKL's point). As an example 10-10-10 (or 24-4-4 or X-X-X) is a balanced fertilizer because it has all three of the main elements a plant needs to grow, Nitrogen, Phosphorous and Potassium (N-P-K per the Periodic Table). The numbers indicate the percentage of each element in the package by weight, so 10-10-10 is a balanced fertilizer with equal weights of N-P-K. 24-4-4 is also a balanced fertilizer, but with 6 times the amount of nitrogen than Phosphorous or Potassium. 0-10-0 (Super Phosphate) is not a balanced fertilizer because it does not have Nitrogen (first zero) or Potassium (second zero).
Nitrogen primarily helps a plant grow green stuff above ground. The more Nitrogen, the more leaves, the more leaves, the more twigs. The more inorganic (or chemical, like Miracle Gro) the nitrogen source, the more vigorous and therefore more course the growth. This is good for young plants you are trying to develop quickly. The more organic the nitrogen source, the more moderate the growth. This is good for more developed plants you are trying to refine.
Phosphorous primarily helps a plant grow roots, and for flowering plants more flowers too. Super Phosphate is used for exactly those reasons by some landscapers as a soil amendment when they plant trees and shrubs (help the plant grow new roots to establish itself) or homeowners when they plant daffodil bulbs (help encourage future flowering).
Potassium primarily helps a plant to be more generally healthy and for flowering plants to have bigger, more vibrant flowers.
All three elements help the plants in other ways, but the above is what you really need to know and can be summed up as Up, Down and All Around with Nitrogen being the Up, Phosphorous being the Down and Potassium being the All Around.
Additionally, there are trace elements in some fertilizers. Look them up yourself. Trace elements are needed in extremely small amounts as the name would indicate. They do various things to help plants. Look those up yourself too.
Finally, if over applied, main and trace elements can damage or even kill a plant, so be careful what you apply, when you apply it, how much you apply and how often you apply it.
Regards,
Martin