Indeed you can "and probably should" break up your code into pieces.
Personally I use simple include() files that contain set of functions for whatever I want to do. One for SQL operations, one for printing website layout elements, authorization etc.
Like Patrick said, it makes it a lot easier to change something about your website for example.
If you have one function that prints the top of the page, and you call that function on each page you print, then changing that function changes the top of every page.
The only drawback of this method is that the more files you include, the more work PHP has to do to read them.
Sometimes breaking up the code is done to decrease the amount of code parsed by PHP when the script is loaded, but if you include 4 large libraries because you need 4 small functions.... you get the idea.
