A theory is a human mental creation that explains facts and has withstood the test of experiment. This view of the nature of science and of theory is owed to philosopher of science Karl Popper. A theory in science has descriptive, predictive and explanatory power. That is, a theory describes the world as we see it and experience it. It allows us to reliably predict how the world will behave in future in a particular set of circumstances, and it explains why the world is as it is. If we make a prediction using a theory, and then conduct the experiment and the prediction fails – the world does not behave as the theory leads us to expect – then Popper would say the theory has been ‘falsified’ and should be discarded. The theories that make up science at any given moment are the ones that have been tested many times and have never been falsified. Einstein neatly summed up Popper’s perspective: “No amount of experimentation can ever prove me right; a single experiment can prove me wrong”.
First, while the Popperian view of science is sort of OK to start with (falsifiability does play an important role in the natural sciences), it doesn’t accurately describe the actual practice of science. (See for example this past discussion.) Well-established theories don’t simply get discarded the moment something appears to falsify it. Otherwise experiments looking for dark matter and supersymmetric particles would have stopped a long time ago. Instead, they usually get modified with some parameter adjustments and/or ad hoc hypotheses, or the experiment itself is re-analyzed, re-done, or simply set aside, if it turns out to be non-repeatable. I can easily give you several more examples just from my sub-field where this is the case. I think a Bayesian view to characterize the belief of the scientific community in a theory is more reasonable here: a well-established theory needs a solid amount of experimental evidence against it before people would consider overturning it.
Second, the above definition of “theory” is I guess one definition that is often used when debating with creationists, but in real life scientists (speaking especially for physics) use the word “theory” in a much looser way. Theory is simply a mathematical framework to characterize and explain some phenomenon in nature. A theory is usually well-motivated, as it has to explain some known facts (at least within its historical context), but it can also have various levels of experimental evidence. In contrast, the above definition seems to imply that Einstein’s General Theory of Relativity was not a theory until Eddington’s experimental test in 1919. But I don’t think that makes sense! For example, Einstein titled one of his papers “The Formal Foundation of the General Theory of Relativity” in 1914, five years before Eddington’s experiment. He didn’t call it the “General Candidate Theory of Relativity”, which was then changed to “General Theory of Relativity” after it became accepted! That’s also why today we have “string theory”, “M-theory”, “supersymmetric theories”, none of which have “withstood the test of experiment”, yet we call them theories anyway.