The ''TV out'' connection that you have allows you to display something (your desktop, a DVD, etc) from your computer on your TV instead of, or in addition to (depending on the software), your computer monitor. In order to watch TV on your computer, you'll need a TV Tuner card (or a USB-based tuner device), which gives you a TV-in connection.
These come in both ATI (All-In-Wonder series) and Nvidia (Personal Cinema series) varieties, and in multiple formats (PCI card, AGP card, and USB "box"). If you want, you can even get a TV Tuner/graphics card combo, or one designed for receiving HDTV as well. However, since there are so many "flavors" of PC TV tuners available, I suggest checking Circuit City's website (they have a pretty good selection) and comparing them, along with their user reviews.
However, I'd like to point out a couple of things about ATI. First, their software is only so-so, so you'll definately want either Microsoft Windows Media Center or a third-party application. (I recommend the free program GB-PVR) Also, the drivers seem to occasionally have problems with AMD processors. (They were designed around Intel's specs.) I haven't tried the Nvidia line, but I've heard those tuners come with better software and aren't quite as buggy.
Hope this helps,
What would I need to be able to watch cable TV on my computer?
My motherboard, an Asus A7N8X has a connection near the 20 pin connection that is labaled as a TV Out connection.
What can I do with this?