Why is it important to understand the relationship between Politics, Commerce and Science?

The main importance is that all three of these things interact and their interaction impacts our lives in a very major way.  Governments and people need to understand the relations so they can try to manage them for the best.  As an example of this, look at the idea of global warming.

Science tells us that global warming is going to be a major problem.  However, the immediate needs of commerce are threatened by this idea because serious action to combat global warming would require things to be done that would alter the current structure of commerce.  Because of this, politicians are pressured to try to control the science or the commerce or both.

So in this case, the relationship is that science threatens commerce which puts pressure on politicians to mediate the dispute. If we don't understand this relationship, we cannot fully understand the problem or its potential solutions.