Mosaic, the creation of Marc Andreessen and Eric Bina, wasn't the first graphical web browser. That honor goes to ViolaWWW. This browser, however, only worked on Unix workstations using the X Windows System. Cello was the first graphical web browser for Windows. Be that as it may, no one argues that Mosaic was the first truly popular web browser.
That's not to say that Mosaic was easy to use. It wasn't. In the early to mid 1990s, simply getting on the internet was still something of a black art. Windows, for example, didn't natively support the internet's fundamental protocol, TCP/IP, until Windows 95 appeared. If you wanted TCP/IP on Windows before that, you needed to use the arcane but absolutely vital Trumpet Winsocket program, and find an internet service provider (ISP).
It was worth it, though. In those early days, people were frantic to get on the web, and Mosaic, a freeware browser, was far more often than not the first browser they'd use. Andreessen and Bina, no fools they, saw the business possibilities on the web and took the Mosaic code base. In October 1994, they turned it into the first successful commercial web browser: Netscape.
Microsoft, which had been slow off the mark to realize how important the internet and the web would be, also used the Mosaic code base, via a company called Spyglass, to make the first version of Internet Explorer (IE). IE 1.0 was released in as an add-on to Windows 95 in the Microsoft Plus package in August 1995.
So it was that by the mid '90s, Mosaic had become the most popular web browser of the early internet years. Indeed, even now, while the program itself is an anachronism, you can still see how its basic design decisions have strongly improved today's web browsers such as Firefox, its most direct descendant, Chrome, and IE.
It may have been 20 years since Mosaic has been released, but we're still seeing its influence today.