At a fundamental level, it's the "standing on the shoulders of giants" concept - to quote wikipedia: It's what humanity did ever since we could pass along information and ideas, at least until artificial restrictions like intellectual property came along.

On a more practical level, open means that bugs can be fixed and features added by anyone. Even if you don't have the time and skills to do it, someone else probably will. Closer to home, search bugs.maemo.org for keyword "patch" and realize that only open components can be fixed by the community.

Some high-profile projects that have really changed things include asterisk, apache, mysql, openoffice, high-level languages like perl, python & ruby, and even full blown desktop environments like GNOME and KDE.

But it's not even about complete projects, think "building blocks" instead - projects like the linux kernel, gcc, openssl, busybox and/or the various GNU *utils, X11, GTK+/QT, libjpeg, libpng, openssl, gstreamer and so on. The more closed components you have in the stack the harder it is to fix things and the greater the chances that the project will eventually disappear into obscurity.