<p>Can anyone provide a clear explanation / example of what these functions do, and when it's appropriate to use them?</p>

Straight from
the manual
...
We know that the foreign keys disallow creation of orders that do not relate to any products. But what if a product is removed after an order is created that references it? SQL allows you to handle that as well. Intuitively, we have a few options:
Disallow deleting a referenced product
Delete the orders as well
Something else?
```
```
CREATE TABLE order_items (
 product_no integer REFERENCES products ON DELETE RESTRICT,
 order_id integer REFERENCES orders ON DELETE CASCADE,
 quantity integer,
 PRIMARY KEY (product_no, order_id)
);
```
```
Restricting and cascading deletes are the two most common options. RESTRICT prevents deletion of a referenced row. NO ACTION means that if any referencing rows still exist when the constraint is checked, an error is raised; this is the default behavior if you do not specify anything. (The essential difference between these two choices is that NO ACTION allows the check to be deferred until later in the transaction, whereas RESTRICT does not.) CASCADE specifies that when a referenced row is deleted, row(s) referencing it should be automatically deleted as well. There are two other options: SET NULL and SET DEFAULT. These cause the referencing columns to be set to nulls or default values, respectively, when the referenced row is deleted. Note that these do not excuse you from observing any constraints. For example, if an action specifies SET DEFAULT but the default value would not satisfy the foreign key, the operation will fail.
Analogous to ON DELETE there is also ON UPDATE which is invoked when a referenced column is changed (updated). The possible actions are the same.
edit:
You might want to take a look at this related question:
When/Why to use Cascading in SQL Server?
. The concepts behind the question/answers are the same.