These modules use the global MathJax object to determine what you want loaded, and alter that object to include the methods and objects that they set up. The initial value of MathJax is saved as MathJax.config, and other properties are added to MathJax depending on the components that get loaded. For example, the startup component adds MathJax.startup(), which contains the objects that the startup module creates, like the input and output jax, the math ocument object, the DOM adaptor, and so on. See the MathJax API documentation for more information.
The MathJax variable can also contain configuration blocks intended for individual components when they are loaded. For example, it can have a tex block to configure the input/tex component. See Configuring MathJax for more details.
Note that you must set up the global MathJax object before loading MathJax itself. If you try to that afterward, you will overwrite the MathJax variable, and all the values that MathJax has set in them. See the Configuring MathJax After it is Loaded section for more about how to change the configuration after MathJax is loaded if you need to do that.