We can dismiss the most common daily life sort of usage -- a theory is something that is false. It's used in comments like 'That may work in theory, but it doesn't work in practice.' If we're talking about what happens in practice, we're talking about what happens in the real world. Scientific theories have to apply to the real world. If your idea makes false predictions about the real world, then the idea is (at least partly) false. And, if your idea consistently makes false statements about the world, then it is not a theory, or even a hypothesis. If there is a scientific theory of climate, it must be making true statements.
We can also dismiss the next most common daily life usage -- a theory is a WAG (wild guess). A common sort of theory of this type is where I, for instance, theorize that since the last time I took my car to the shop, it got good service, that the next time I go, it will as well. There's really very little data behind that thought, and very little analysis. But it seems like a reasonable sort of statement. Or the 'lucky socks' theory sports fans or athletes might have. Their team won the last time they wore a particular pair of socks, so they theorize that the team will win again (or at least have a better chance of winning) if they wear the same socks for today's game. Again, it seems reasonable to the person making the statement, but there's little data behind it and little analysis.
Now to consider the more difficult waters, where I hope that the two philosophers I know sometimes read will comment with appropriate corrections and elaborations.
One part of math/engineering/science usage is that, in contrast to common usages, a theory is a very good thing indeed. Actually the best you can get. Some other terms you'll hear are conjecture, hypothesis, and law. The 'good service' or 'lucky socks' theories, as we'd term it in common conversation, are really more in the nature of a conjecture. We've got very little data, and very weak chains of reasoning. But, hey, it looks ok. After you collect more data and get stronger lines of reasoning, you have a hypothesis. It's also better if the hypothesis covers more situations than the conjecture. Get to the point of covering many situations, with very strong evidence and very strong lines of reasoning, and you finally have a theory.
Law is a different kettle of fish entirely. In terms of how we do science any more, it's also an anachronistic term -- something that used to be used, but now is uncommon. Laws, in my areas at least, are simple mathematical relations between a couple of things. Newton's Law of Gravitation, for instance, says that the gravitational force between two bodies is proportional to the product of their masses divided by the square of their distance. Simple relation and it's even reasonably correct. Hard for you to test for yourself, so I'll mention another one. Hooke's law of elasticity. This says: take a spring (or rubber band, or piece of elastic, or bungee cord, ...) and hang it up. Measure where the end is. Now put a small known weight at the end and measure how much longer the spring gets. Add a second weight, equal to the first. You'll see (says the law) the spring lengthen by exactly the same amount as before. This is reasonably correct as well. But as you keep increasing the weight, you'll eventually see the distance the spring lengthens start to change, and eventually it changes quite dramatically -- if you put enough weight on the spring, it will break. Laws in this sense are convenient expressions of relations. You can use them, within limits. But there definitely are limits and, often, even the proposers knew about the limits (I think Hooke did).
One place you can see the change in how scientists think/thought about Law versus Theory is that Newton's Law of Gravitation (1600s) was replaced by Einstein's Theory of General Relativity (1910s).
Within the realm of scientific theories, though, there are two different sorts. I'll call them the elegant and the complex. We mostly think about the elegant theories when we think about scientific theories. The theory of evolution, for instance, is an elegant theory. Its elegance lies in the fact that it covers an enormous range of observations, can be used to make a large number of predictions, and, yet, can be stated in a page.
I don't believe there is an elegant theory of climate. It is of the complex theory sort. I have in my library, for instance, a book on Number Theory, and one on Theory of Flight. In neither will you find a one page description of the Theory of Numbers, or the Theory of Flight. The sense of theory involved is 'a body of principles and understandings that apply to a given subject'. It's an elegant theory when the number of principles or understandings is small. And, for something like flight, or numbers, and on for many areas, you have quite a few principles to work with.
In climate, some of our principles, or statements of theory, would include:
- Conservation of mass applies to the climate system
- Conservation of momentum applies
- The laws of thermodynamics apply
- The general theory of relativity applies
- Quantum theory applies
- Tectonic theory