Explaining classes can be lengthly, I send you to the http://processing.org/learning/objects tutorial.
But explaining the difference between functions and methods needs that you understand classes...

Oh well, just covering the bases should lighten some things.

You don't use a class "rather than a function". You use a class when you need an object. Which is the official word for class instance. Think of classes like a blueprint: you define variables (named 'fields' here) and functions (named 'methods' in this context). Then you instance the classes to objects, you make several of them using the class definition as a mold.

Simple (simplistic) example:

1. class Person
2. {
3.   // Fields: the data associated to the object
4.   String name;
5.   int age;
6.  
7.   // Constructor: you create objects by calling this special function allowing to initialize the data
8.   Person(String n, int a)
9.   {
10.     name = n;
11.     age = a;
12.   }
13.  
14.   // Methods: these are simple functions, but acting only on the object from the class they belong to
15.   void makeOlder()
16.   {
17.     age++;
18.   }
19.  
20.   // Polymorphism: same name, different parameters
21.   void makeOlder(int n)
22.   {
23.     age += n;
24.   }
25. }

Then you create objects like: Person employee = new Person("John", 32);
and you invoque methods like: employee.makeOlder();

Somehow, functions are a concept from other languages like C or Basic, they don't really exist in Java, but Processing re-created them by using a simple trick (beyond this discussion), so you can just call fill(200) instead of g.fill(200) for example. Ie. they are called without an (apparent) object.