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I am fairly confident that these are Processing specific...

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ArrayLists are Objects (Lightweight Components) that extend the functionality of Arrays and add more Java-style features (such as getter/setter methods, arbitrary, combined object types and better exceptions etc). In order to instantiate an ArrayList you must create a new one with the 'new' operator, just as you'd do with any other object:

ArrayList foo = new ArrayList();

In order to create a n-D ArrayList you must create an ArrayList that contains ArrayLists. For 2-D eg. you'd make an arrayList that contains ArrayLists which contain your objects. For higher dimensions, more levels of nesting are required. Or you can just build your own class that takes indices as parameters and does the dirty job for you.

In general arrayLists are more flexible, but that goes in expense of computational time for access, storage etc, since more things need to happen to access or modify a variable list with arbitrary components than a fixed-length fixed-type one.

To sum up: Use ArrayLists for flexibility and arrays for speed.

Or, as you said, you can use ArrayLists where you need to do heavy modifications and then switch back to arrays for speed.