Which computer software was associated with this logo?

This was an original logo of the Mozilla browser. The Firefox project began as an experimental branch of the Mozilla project by Dave Hyatt, Joe Hewitt, and Blake Ross. They believed the commercial requirements of Netscape's sponsorship and developer-driven feature creep compromised the utility of the Mozilla browser.

The Firefox project has undergone several name changes. It was originally titled Phoenix, which carried the implication of the mythical firebird that rose triumphantly from the ashes of its dead predecessor, in this case from the "ashes" of Netscape Navigator after it had been killed off by Microsoft Internet Explorer in the "First browser war". Phoenix was renamed due to trademark issues with Phoenix Technologies; the replacement name, Firebird, provoked an intense response from the Firebird database software project. In response, the Mozilla Foundation stated that the browser would always bear the name Mozilla Firebird to avoid confusion. After further pressure, on February 9, 2004, Mozilla Firebird became Mozilla Firefox.