KWRBT, here's what I think he means by straining the soup.
When you make soup, and then refrigerate it overnight, a layer of fat will form overnight. When you go to reheat the soup, simply spoon off the layer of fat, and you have low fat soup.
That is partly what I mean. Removing the coagulated fat from the top is a must (unless you like greasy, fatty soup). However, remember I said to leave the liquid, chicken and vegetables in the pot overnight. So the other part of it is to use a strainer to catch all the solid stuff and retain only the liquid. As for whether or not that is the soup, actually what you have there is chicken broth. If you want to only have clear chicken broth as your soup, then you are done. However, you can add vegetables, rice, noodles, etc...really whatever you like to "make the soup". It's totally up to you. If you add additional items, the soup only needs to cook long enough to cook those items since it already has all the flavor it needs.
One other thing that I should clarify. When you cook the chicken in the pot, use a chicken carcass because you will be cooking the liquid for hours. If you cook the whole chicken and then plan to add some of the meat in your final soup, the meat will probably be a little tough. What I actually like to do is roast a chicken, have a nice chicken dinner, remove most of the remaining meat, then make the chicken broth with the carcass and use the remaining meat in the final soup.