I have one of this connectors on my sound card. what can I use this for? can I plug in my home stereo into it and listlen to sounds from my computer in the stereo? thankx in advance.

Basically, yes.

Its a optical conection BTW...

They can also be coaxial connectors rather than optical. They produce digital output so your stereo needs a spdif input, you can't just hook it up to the line in.