Here, I made up a couple crude images which might help.
No Capture Card.png
This is what the average home entertainment setup looks like. Multiple video sources feeding in to a television, usually with the PC as a separate unit.
With Capture Card.png
This is what it looks like with a capture card in the mix. You can add the capture card in to any of the systems that feed the television, but only one at a time. So if you want to record from your gaming console, you'd have to plug the capture card into the gaming console, instead of the cable box. Then just switch it again whenever you're ready to record from a new source.

Now, if your television generates an image on its own, if you have a Smart TV connected to the internet that handles your Netflix or whatever, you might NOT be able to record from that. That would depend entirely on if your TV has a video out capability, and I'd need to know what sort of TV you have to tell you that.