One of the founders of the open source movement, Bruce Perens, who had previously drafted the Debian Free Software Guidelines (which would be adapted to become the OSD), puts the date at February, 9, 1998, when he published an announcement of the OSD.
Debian is one of the early distributions of Linux. Free and open source software meant anyone could fix problems should they be discovered. It also mean making derivatives was possible with packages like archive tools which can then provide backwards compatibility bundled with new functionality.
Before Linux surfaced the open source community used FreeBSD which provided developers an open platform that could better leverage modern processors and hardware.