Tropical rain forests are one of the most bio-diverse and biologically important areas on the planet. Much of their animal and plant life is unique and unreproduced anywhere else. Logging and agriculture are the two largest influences on the rain forest, causing many thousands of acres to become either deforested or even barren. Rain forests are the largest land-based plant systems for the water and carbon cycles in the atmosphere and groundwater; removing more and more of the rain forest causes the carbon cycle to become unbalanced, with not enough carbon dioxide converted back to oxygen. This could substantially affect the air quality of the atmosphere in the future.
Another significant effect of deforestation is the loss of unique plants and animals. To date, there are many undiscovered plants deep in the rain forests, and many that have become entirely extinct without ever being cataloged. By finding and analyzing different properties of these unique plants, it is possible to create new medicines and new compounds. Many of these plants have been used in their natural form by indigenous peoples for years, but if those plants are destroyed, both the future medicines and the current uses are lost.
Since we rely heavily on deforestation, when it is all gone, our future generations will not be able to rely on it anymore. This affects us greatly.