Since I've been reviewing The God Delusion I have been thinking quite a lot about the role of science and religion and how the two relate. It isn't always easy to separate scientific and religious truth claims. There isn't a simple bright line that neatly divides the two fields. Still, it is important to understand what divides the two fields, and how to reasonably draw a line between them.
The best way to do that is to look at the goals of science and religion. Although at times they both tackle the same subjects, both fields have very different goals. Simply put, the goal of science is to provide an explanation, and the goal of religion is to provide a justification.
What do I mean by that? Well, first of all, an explanation is a descriptive model. The goal of an explanation is to provide an understanding of what is happening in a given situation. If our understanding is very good, we should even be able to predict what will happen in certain situations.
Scientific explanations also tend to be reductionist in nature. They explain complex phenomena in relatively simple terms. For explanations, the goal is always to make things as simple as possible, so they can be more easily understood. If the explanation is more complex than the thing you're trying to explain, then it's not a very good explanation.
Justification, on the other hand, works differently. Instead of trying to understand the universe in terms of simpler things like particles and forces, a justification seeks to understand how the universe relates to more complex things, typically God. A justification is able to explain, not just how the universe operates, but how it came to exist, why it is the way it is, and what purpose it has.
Unsurprisingly, most atheists don't think the universe needs any justification. The famous atheist philosopher Bertrand Russel once said, "The universe is just there." To put it another way, the atheist position is that the universe is self justifying. I have my issues with this, which I've been over many times before. For now I will just conclude with one of my favorite xkcd quotes, "If the question of what it all means doesn't mean anything, then why do I keep coming back to it?"
In any case, I hope this helps you to understand the difference between scientific and religious theories. It may also shed light on many of the conflicts between science and religion. I think it's also helpful for anyone who wants to try to separate out scientific ideas from religious ones. This is useful for anyone who struggles to see how scientific and religious ideas can operate together without one trampling all over the other.