The definition of science poses some problems for people. Everyone seems to have an idea of what science is, but articulating it is difficult. Ignorance about science isn't a viable option, but unfortunately it's not too hard to find religious apologists spreading misunderstanding. Because science is best defined by scientific methodology, an accurate understanding of science also means understanding why science is superior to faith, intuition, or any other method of acquiring knowledge.
Science & Definition
The classical definition of science is simply the state of "knowing" — specifically theoretical knowledge as opposed the practical knowledge. In the Middle Ages the term "science" came to be used interchangeably with "arts," the word for such practical knowledge. Thus, "liberal arts" and "liberal sciences" meant basically the same thing.
Modern dictionaries are a bit more specific than that and offer a number of different ways in which the term science can be defined:
The observation, identification, description, experimental investigation, and theoretical explanation of phenomena. Methodological activity, discipline, or study An activity that appears to require study and method
For many purposes, these definitions can be adequate, but like so many other dictionary definitions of complex subjects they are ultimately superficial and misleading. They only provide the barest minimum of information about the nature of science. As a consequence, the above definitions can be used to argue that even astrology or dowsing qualify as "science" and that's simply not right.
Science & Methodology
Distinguishing modern science from other endeavors requires focusing on scientific methodology — the means by which science achieves results. Fundamentally, then, science can be characterized as a method of obtaining reliable (thought not infallible) knowledge about the universe around us. This knowledge includes both descriptions of what happens and explanations of why it happens.
Knowledge acquired through the scientific method is reliable because it is continually tested and retested — much of science is heavily interdependent, which means that any test of any scientific idea entails testing other, related ideas at the same time. The knowledge is not infallible, because at no point do scientists assume that they have arrived at a final, definitive truth.
The knowledge acquired through science is about the universe around us, and that includes us as well. This is why science is naturalistic: it is all about natural processes and natural events. Science involves both description, which tells us what has happened, and explanation, which tells us why it happened. This latter point is important because it is only through knowing why events occur that we can predict what else might occur in the future.
Science can also at times be characterized as a category or body of knowledge. When the term is used in this manner, the speaker usually has in mind just the physical sciences (astronomy, geology) or biological sciences (zoology, botany). These are sometimes also called "empirical sciences," as distinguished from the "formal sciences," which encompass mathematics and formal logic. Thus we have people talking about "scientific knowledge" about the planet, about stars, etc.
Finally, science is often used to refer to the community of scientists and researchers who do scientific work. It is this group of people who, through practicing science, effectively define what science is and how science is done. Philosophers of science attempt to describe what an ideal pursuit of science would look like, but it is the scientists who establish what it will really be. In effect, science "is" what scientists and the scientific community "do."
This brings us right back to science being the scientific methodology — the method and practices used by scientists to acquire reliable knowledge about the world around us. The superiority of science over other attempts to acquire knowledge lies in that methodology. Developed over the course of many decades, the scientific method provides us with information that is more consistently reliable and useful than any other system that humans have ever tried to develop — including especially faith, religion, and intuition.