It was Internet Explorer. But, what was probably confusing about it was that anything that required Internet access would start up the program that dialed the modem and connected to the Internet. So, clicking on the icon would eventually launch the browser, but first it would launch the dial-up program, which would take about 30s to connect.

As an aside, it really grates to see how Microsoft called their browser "The Internet". And that's the least dastardly thing they did that let them use their monopoly on operating systems to destroy Netscape.

The original "Internet Explorer" icon was a globe and magnifying glass, with the text "The Internet," underneath