What is a "swing" applet?  Many Java programming web sites mention
them but I'm having a difficult time finding a definition for "swing".

Hello:

Swing applet: A Java applet that uses swing classes

Take a look to the links below to know more about swing

Introduction to Swing
http://www.cs.earlham.edu/~jimg/mozart/presentation/swingintro.html

* Swing is a subset of the Java Foundation Classes (JFC)
* The name "Swing" is not an acronym
* An effort to incorporate many of the features in Netscape's IFC as
well as some aspects of IBM stuff
* First released in March of 1998 with nearly 250 classes and 80
interfaces
* Swing is not a replacement for the AWT.
  - Needed to support truly architecture independant interfaces
  - Contains more powerful components
* Why bother?
  - Increased acceptance (many more supported architectures)
  - AWT based on architecture-specific widgits.

JAVA FOUNDATION CLASSES (JFC)
http://java.sun.com/products/jfc/

"These components are written in the Java programming language,
without window-system-specific code. This facilitates a customizable
look and feel without relying on the native windowing system, and
simplifies the deployment of applications."

Running Swing Applets 
http://java.sun.com/docs/books/tutorial/uiswing/start/swingApplet.html

The Swing Connection
http://java.sun.com/products/jfc/tsc/

Swing: A Quick Tutorial for AWT Programmers
http://www.apl.jhu.edu/~hall/java/Swing-Tutorial/

Hello World Swing Applet
http://www.fluffycat.com/java/JavaNotes-HWSwingApplet.html

I hope it helps!

Regards.

Note that most modern browsers will NOT run Swing applets unless
they're equipped with Sun's Java plug-in.  Swing is an improvement
over AWT (Awstract Windowing Toolkit), and it's pretty nifty, Swing
classes take the names of AWT classes, but with a J at the beginning
(i.e. JApplet, JMenuBar, etc.).