When using Internet Explorer a revolving ball will appear.  Sometimes
it is black and white and sometimes it is rainbow colored.  Does this
revolving ball have a name?  What is the meaning of the different
color patterns?

Hello beany2788-ga

The Internet Explorer (IE) revolving ball is usually called the
THROBBER (in my version of IE it is a small waving Windows flag).

It is used primarily by companies to brand the copy of Internet
Explorer that you are using but of course this is also something you
can do yourself very easily.  Its function is simply to tell you that
the IE is performing a task, for example when the throbber is animated
it is loading a page.  The black and white color you sometimes see is
simply part of this animation and does not indicate anything in
particular.

There are a number of excellent tutorials that discuss the
customization of IE and how you can get it to look.  As a starting
point I have indicated a number below that specifically reference the
throbber:

http://www.pcanswers.co.uk/tips/default.asp?pagetypeid=2&articleid=30521&subsectionid=616
http://www.g4techtv.com/screensavers/features/41389/Windows_Tip_Customize_Your_IE_Logo.html
http://webjunction.org/do/DisplayContent?id=1306
http://www.virtualplastic.net/html/logo_thr.html#throbber
http://www.tweakxp.com/tweak1169.aspx
://www.google.com/search?q=%22internet+explorer%22+throbber

If you have any further queries on this subject please ask for
clarification and I will do my best to respond swiftly.

The version of IE I believe you are using is for Mac OS X.  The
spinning ball is generally referred to as a wait cursor, or a busy
cursor.  It lets you know the program is doing something and won't be
able to respond.  It is more humorously called the "Beach Ball."  If
your whole computer stops responding and all you can do is move the
"beach ball" around, then this is referred to as the "Spinning Ball of
Death" (SBOD).  This last comment is less prevalent in newer versions
of OS X.