According to NASA, humans explore because of an innate desire to learn the world around them. The urge to explore was ingrained in the psyche so that human ancestors could find places that were abundant in food, water and other resources necessary for survival. This primordial desire to explore the world around them might be what continues to lead humanity to venture out and explore even today.
NASA argues for this line of reasoning by stating that society has been reaping the benefits of human exploration for centuries. Expeditionary missions that were sent out to find shorter routes to the Indies ended up with humanity discovering and later colonizing the New World. In that same vein, exploratory efforts made to uncover the nature of the cosmos have led to profound discoveries regarding how the universe works.
The benefits that are reaped by exploratory efforts need not always be abstract and intangible. Developments that might initially be made for space exploration often end up benefiting human beings on a daily basis. For example, cellular mobile technologies would not have been possible were it not for satellite communications paving the way for their conception. Given the immensity and difficulty of the undertakings, exploratory efforts also encourage cooperation between governments and people.