You earn money on HubPages when you publish an article and people read it. There are ads displayed on the article, and you receive a small payment for every pageview. In addition, you can include special advertisements (links to Amazon and eBay) in your articles, and you'll earn commission if people click on those links and buy things.
The reason you see this posted on job sites is that HubPages also has a referral program. If I post a link on a job board and you follow it and sign up, I'll receive a small commission based on how much you earn.
That being said, you'd have a hard time making a "living" on HubPages. Depending on some random factors, you'll earn $2.00 to $3.00 per 1,000 views on your hub. A successful hub will probably get about 1,000 or 2,000 views every month. That means a "good" hub will earn you a couple bucks a month, but a flop will earn you next to nothing.
To make a very meager living ($1,000) month, you'd have to publish a few hundred good hubs. A realistic goal is to make some pocket change ($50, $100, maybe a few hundred bucks) a month with some hard work and patience. While I wouldn't say it's impossible to earn $1,000+, that would put you in a very select club.