The Banner Module and Component that comes installed with the basic Joomla Install is:

very useful
simple
limited

The Banner Module and Component are useful if you want to place a changing graphic image on your site and track some simple usage statistics on it. You can use it to monetize your site and sell banner ads, or you can use it to highlight other features or pages within your site.

Like most Joomla add-ons, there is a component and a module. The Banner Component allows you the set up, assign and prepare basic publishing information about a banner and the associated client. The module, then uses the component information for front end display.

The banner module displays, at random, a new banner every-time the page reloads. You cannot predetermine the ordering, but you can set a banner to display only a selected list of clients. You can copy the banner module a number of times and assign it to other pages and clients. For example, high visibility clients on the Home page, and secondary clients on other pages.

Other behaviors or Features are

upload banners / images (any number)
assign a banner to a client
set the number of times a banner is viewed (impressions purchased)
publish/unpublish
assign a banner to a url when it is clicked
show the number of impressions (views) and click throughs
allows for custom code to be assigned to a banner (e.g. affiliate tracking code)

There are a couple of tips that may help to fix problems or make it more usable.

Banner Module Tips

Be sure to publish the banner module once you upload your images and assign them to a client
Use PNG files with a background of "transparent"
- if you use "white" it may not look good on your site's template
- a colored background may hide other content from other modules
- try using Gimp - it is an excellent Open Source (free) image manipulation program that rivals PhotoShop.
filenames are important to the banner module. It only likes alpha/numeric - take out spaces, and underlines
Before you create a number of images or banners, be sure to understand the size constraints (i.e. width and height)
You can copy the banner module a number of times and assign the module to display at different module positions or different pages

Try this little gem. Below is a Custom Google Search pointing to the Extensions area on Joomla.org. It works much better than their own search function.