You can find many reasons from different sites. Here I list 6 most persuasive reasons:
1. Understanding and Protecting Our Planet
NASA’s Earth Science division aids us in understanding the amazingly complex planet we inhabit.
Examining other planets such as Mars and Venus helps us recognize just how unique Earth is, and provides examples of how a planet’s climate can shift.
NASA funds research to search the atmosphere for hazardous asteroids and sends missions to those asteroids to learn about how we could prevent them from colliding with our planet if we ever need to.
2. New Technology
Space exploration unites many intelligent individuals from different fields and has them working together to solve challenging problems. The result is not only great scientific findings, but also lots of useful inventions. From improved baby food to better cancer diagnostic technology, NASA’s technology is everywhere.
3. Answering Big Questions
How did the universe come to be? How did life originate? How was our planet made? Are we alone in the universe? Generations have been asking these questions since the beginning of time. The fact that we even ask these questions is a demonstration of human brainpower. Because now have the intelligence and bravery to explore the universe, we can discover the answers.
4. International Cooperation
Space exploration projects are most often the outcome of international collaboration. The International Space Station is the most prolific example, but the space shuttle often has astronauts hailing from different nations, and several robotic missions incorporate technology built by teams from different countries. As NASA prepares to return to the moon, missions from all over the world are already in orbit, or already planned. Future Mars missions will almost definitely include multiple space organizations to distribute the expense among numerous nations.
5. Long-Term Survival
Right now, all of humanity’s eggs are contained in the basket known as “Earth”. It’s only a matter of time before devastation befalls our planet and the life of humanity is completely changed. Whether that disaster is environmental, like a stray comet, or self-inflicted, like a nuclear war, it’s conceivable that our planet will someday be inhabitable. What will happen to all the achievements of generations of our species? All of our art, literature, science, even our genes could be destroyed. However, we would be preserved if there were humans alive elsewhere in the solar system. Space exploration and eventually, colonization of Mars and the Moon are like protection for our species and its achievements.
6. Natural Resources
Due to over population, we are quickly depleting our planet’s environmental resources. In space, however, there are practically limitless resources. It’s a matter of gathering them and transporting them back to Earth, which will certainly be a difficult task. Nonetheless, there will be no more reason to continue raising the prices on oil, although ideally we will no longer need oil at some point.
Reference:
http://science.howstuffworks.com/10-reasons-space-exploration-matters.htm