Please explain (with examples) what is meant by A/B testing of a website.
In the context of a web site it means that some users of the site/webapp get slightly modified version(s) and you verify how each modification affects the usability/user's behavior compared to baseline "control" version.
As always with A/B testing, which is a statistical technique, you need a large enough sample to properly assess impact of change.
This was done by both Amazon and Google among well known web companies.
A VERY good article (with marketing angle) on web A/B testing is : http://www.clickz.com/3349901
In the interest of completeness, here's the full A/B testing definition from Wikipedia:
A/B testing or bucket testing is a method of marketing testing by which a baseline control sample is compared to a variety of single-variable test samples in order to improve response rates. A classic direct mail tactic, this method has been recently adopted within the interactive space to test tactics such as banner ads, emails and landing pages.
Significant improvements can be seen through testing elements like copy text, layouts, images and colors. However, not all elements produce the same improvements, and by looking at the results from different tests, it is possible to identify those elements that consistently tend to produce the greatest improvements.
Employers of this A/B testing method will distribute multiple samples of a test, including the control, to see which single variable is most effective in increasing a response rate or other desired outcome. The test, in order to be effective, must reach an audience of a sufficient size that there is a reasonable chance of detecting a meaningful difference between the control and other tactics