The first function in an m-file (i.e. the main function), is invoked when that m-file is called. It is not required that the main function have the same name as the m-file, but for clarity it should. When the function and file name differ, the file name must be used to call the main function.
All subsequent functions in the m-file, called local functions (or "subfunctions" in the older terminology), can only be called by the main function and other local functions in that m-file. Functions in other m-files can not call them.
In addition, you can also declare functions within other functions. These are called nested functions, and these can only be called from within the function they are nested. They can also have access to variables in functions in which they are nested, which makes them quite useful albeit slightly tricky to work with.
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