Science
[edit] Casual Usage
In science the word theory is not a synonym of "fact". For example, it is a fact that an apple dropped on earth has been observed to fall towards the center of the planet but we invoke theories of gravity to explain this occurrence. However, even inside the sciences the word theory picks out several different concepts dependent on the context. In casual speech scientists don't use the term theory in a particularly precise fashion, allowing historical accidents to determine whether a given body of scientific work is called a theory, law, principle or something else. For instance Einstein's relativity is usually called "the theory of relativity" while Newton's theory of gravity often is called "the law of gravity." In this kind of casual use by scientists the word theory can be used flexibly to refer to whatever kind of explanation or prediction is being examined. It is for this instance that a scientific theory is a claim based on a body of evidence.
[edit] Philosophical Conception
This is in considerable contrast to the more philosophical context where a scientific theory is understood to be a testable model capable of predicting future occurrences or observations and capable of being tested through experiment or otherwise verified through empirical observation. As with most things in philosophy there is considerable debate as to whether this is really the correct concept to use in describing scientific research. For instance many definitions also add the constrain that a theory describes the natural world, though it is often unclear whether this is a definition of natural world or a constraint on what can be a theory. Note that this concept specifically does not require that a theory be particularly well supported or have any justification whatsoever. A major concern in this philosophical context is the problem of demarcation, i.e., distinguishing those ideas that are properly studied by the sciences and those that are not. Intuitively one might suppose that it doesn't matter where a suggestion came from, when it was made, or if it was ever well supported by the evidence to whether it's the sort of thing that scientists ought to consider (e.g. test or dismiss as already tested). Unsurprisingly, therefore, this concept of a scientific theory tends to apply equally to justified and unjustified predictions [3]. In other words the term theory is used so that it encompasses what might be commonly called a hypothesis.
[edit] Pedagogical Definition
Finally, in pedagogical contexts or in official pronouncements by official organizations of scientists one gets a definition like the following.
According to the United States National Academy of Sciences,
Some scientific explanations are so well established that no new evidence is likely to alter them. The explanation becomes a scientific theory. In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature supported by facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena, [4]
A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world. The theory of biological evolution is more than "just a theory." It is as factual an explanation of the universe as the atomic theory of matter or the germ theory of disease. Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.