One way to think of it is: a static method or property is effectively a global one. It exists independently of any instances of the class, and so can be accessed without reference to a class instance.
If so why have them? Two main reasons. Because they are part of the class definition they have access to all its properties, including private and protected ones. At the same time they can be accessed by instances of the class, even if private. This can be used many ways.
The other reason is code design. If you e.g. create one sort of object in a factory, or get them from a pool, then create that factory/pool using static properties and methods in the class for that object type.
And you have no choice in Actionscript, as you cannot create independent global methods and properties. Everything is part of a class. You can have classes which are just containers for static methods and properties, like Starling's MathUtil class, but you still need to come up with a class name, put it into a class hierarchy.