OpenSSH was created by the OpenBSD team as an open alternative to SSH, which is now a commercial product. It's claimed that OpenSSH is more secure than the orginal, partly due to the reputation of the OpenBSD developers in emphasising security, and also due to its "open" nature.
The "Open" in the name refers to open source. Although source code is available for the original SSH, various restrictions on its use are imposed. It's open to debate whether this lack of "openness" has any security implications in this case.