The earliest Macs could only do one thing at a time: if you wanted to use a wordprocessor you would have to quit the spreadsheet you were using. Before long though Apple gave us the means to have many pieces of software running at once. Once you can have both a wordprocessor and a spreadsheet (or anything else) running at the same time you need a way to switch between them.
Modern Macs give us the Application Switcher. This is the item at the extreme right-hand end of the Menu Bar.
[Update 2009: In Mac OS X hold down the Apple (Command) key and press the Tab key, as explained in Command Tab. A dark ‘band’ of applications is displayed across the centre of the screen. Press Tab repeatedly to move between applications. Let go the keys when you reach the Application you want. ]
In Mac OS 9
Depending on several things, you might see an icon or some words, or both an icon and words in that place. Whatever you can see, if you click at that place a list of possibilities will show up.
There are three items at the top: Hide XXX, Hide Others and Show All. Below that is a list of all the applications you are running at the moment.
Suppose you have Eudora open at the moment and you also have running Internet Explorer, Appleworks and Simpletext. The Application menu will let you Hide Eudora or Hide all the Other applications. If you now want to use Appleworks (which is already running, after all) just go to the Application Menu and slide down to Appleworks then click.
And if you don’t like all that mousing around: try holding down the Command key (the Apple key) while you press the Tab key. You will cycle through all the open applications in turn.