The study of the heavens and the celestial objects, such as planets and stars, is called astronomy. Understanding what these celestial objects are, what they are composed of, why they move the way they do give us a lot of insight to our own planet Earth and why it does what it does.
If you are asking about applications that were first used in the exploration of space, the list is quite numerous. Take communications, for example. The first communications satellite went into orbit back in the sixties, and we have gone from the use of landline telephones to common use of cell phones, not only to speak to each other, but also fully equipped with internet capabilities. Teflon, which is a nonstick coating applied to cooking pots and pans, had its originations in the American space program. The International Space Station (ISS) is a multinational space institution enabling many nations to benefit and learn from space studies.
Space science is called astronomy.
It's practicle uses are in astrophysics, research regarding life on other planets, and the physical base of origin of mankind. It also includes the experimental research such as of Kalpana Chawala, Neil Armstron etc. where they observed the effect of extra terrestrial on plants and animals. But these fields are very advanced- require a lot of degrees, and qualifications. Genarally people start proffessionally with original thesis and papers on recently discovered stars, planets, and other bodies. It can also be used to predict various activities of earth, estimate distance of stars, their composition etc.