Linda,
Netscape and Microsoft Internet Explorer are browsers - not the only two but the best known. Once you've logged on to the internet, with your dial-up service, cable modem or whatever you use, the browser is the software you use to access the different web sites. In some cases, the browser also helps you read your email and perform other online tasks. Without your browser, you could be online, but not able to do anything useful (like read The Grumble.)
One of the reasons that Microsoft has been in trouble with the Justice Department is that it bundles their browser with the Windows operating system, thereby gaining a near monopoly in the "browser wars" competition. Indeed, each succesive version of Windows is more closely integrated with Internet Explorer so that the distinction between on-line and off-line activities is getting quite blurred.
My motivation behind downloading and installing Netscape as a second browser was very simple. I had installed the newest version of MS Internet Explorer (version 6.0) and my online banking would not yet recognize it for security reasons. "Downgrading" back to version 5.5 is not impossible, but very tedious so I installed Netscape 6.1, which my banking site will work with.
When I'm online, I can use either browser, or both. Eventually my online banking will become compatible with the new MS browser and then I can decide if I want to keep Netscape for its other features, which are considerable.
The reason most of never think about our web browser is that, when we buy a computer with Windows preinstalled, the MS browser is already there - nothing else to install - and most of us use it by default.
Is that sufficiently ambiguous?
(Jerry, feel free to fill in the considerable blanks.)
Ron