It benefits you because when you refinance, you are presented with a $100,000 check, which you use to pay off your $80,000 mortgage. You now have $20,000 to spend on big screen TVs, a “much deserved” vacation, and a big grill for your backyard. Woo hoo! You could also use it to pay off your credit cards, reducing your interest burden from the 10-20% you pay the credit card companies to the 4-8% you pay on your mortgage.
If your home price is increasing, and therefore your home equity, it is a useful way to turn that home equity into cash that you can use for other purposes. In theory, this could be good because it would allow you to rebalance and diversify your total assets. In practice, most people just think of it as free money (since otherwise their home price appreciation is just a paper profit that they can’t spend), which is where the expression “using a home as an ATM” comes in.
Of course, when home prices stop appreciating and go down, this can be really bad on the downside. People may still do a cash out refinance these days, but only if their loan to value ratio is waaay below 80%.