Well, broadcasting usually means doing a live stream, which is why they mention twitch. Youtube videos are usually recorded on your PC and then later uploaded to Youtube (you thus have an opportunity to edit these before putting them online, while live streams are live, your audience sees what you see).
For recording PC gaming videos for youtube I personally use MSI Afterburner, which is a free utility. It has a lot of other bench marking and other stuff built in you might not care about, but it can record in quality that rivals fraps, a paid program. If you don't have a great upload connection you might need to then use another program to compress the raw video so that it doesn't take days to upload to youtube.
