The word "science" comes from the Latin, scientia, meaning "to know"1. Science was originally a branch of philosophy. Some of the great ancient philosophers could be classified as scientists. Aristotle delved into many different sciences. Atomists such as Leucippus and his pupil Democritus were propounding an atomic theory as early as the 5th century BC. As philosophers began to specialize, science began to separate from the more speculative realms of philosophy until, today, few recognize much connection, except perhaps in the realm of cosmology (the study of the beginning of the universe).
Science as a discipline for advancing human understanding has come to rely heavily on a process called the "scientific method". This is a process of hypopthesis and experimentation that produces repeatable, verifiable results. The knowledge base built up using this process pulls science forward, and the knowledge gained is applied by engineers who design modern gadgets we collectively call technology.
Science and technology, together have fueled society's advancement into a cleaner, more efficient and more pleasant world. It is well-demonstrated that technological advances are the main reason that productive industrialized countries such as the United States, Great Britain, Japan, Germany, Australia, and Canada, can produce so much of the world's goods and at the same time maintain a clean and healthy environment.
Two main branches of science have been aknowledged, the natural and the social sciences. The natural sciences are those that do not involve human action and interaction. They include astronomy, zoology, physics, entymology, the study of insects, and many more.
A vital science for understanding life is biology. Basic processes such as the power generating ATP-ADP cycle and osmosis are studied. Beyond laying a foundation for understanding life, biology has even influenced technological inovation. (We can see how man mimics nature with applications such as reverse osmosis.)
Geology studies the Earth, our immediate environs, and encompasses many of the interesting causes of natural disasters such as earthquakes and volcanoes. Earthquakes can be devastating, but the more we find out about the tremblers, what causes them, and how to prepare for them, even something as simple as the application of first aid the less damage they can do. It is said that carbon is the basis of life. Yet in mineralogy it also has a prominent place. Some of the most well-known minerals come from carbon in the form of diamonds and graphite.
Two instruments have largely enabled advancement in the sciences. These are the telescope and the microscope. Although people could make guesses about what lay in outerspace, or how plants and animals function, they could not really understand it, until they could begin to see it with these amazing devices.
The social sciences include history, sociology, psychology, anthropology, economics, and many more topics. The social sciences are not as exact as the natural sciences. Yes, impirical data may be gathered in the form of polling, or done in observation of psychological experiments. Nevertheless, when the human element is added, there will nearly always be an exception to the rules divined by social scientists.
There have been many attempts to make the study of history more rigid. Even Marxist thought as laid out in the Communist Manifesto and "Das Kapital" are intended as a scientific approach to the study of history and economics. Other writers have even dreamed of applying mathematics directly to history in an effort to quantify events, and extrapolate them in to the future. (See the Foundation Series by Isaac Asimov.) Although general theories might be promulgated and be useful (See Plato's "Republic" for example), it is highly unlikely that any kind of calculus will be invented anytime soon that will predict events in a precise manner.
Yet the study of the social sciences have surely advanced society. Fields such as psychology are useful, not merely in understanding human behavior, but also in shaping it in a positive way. A good example is the work of Piaget in child development.
Science then, has been a catalyst for human advancement, helping humans live, healthier and happier lives.