It's shorthand for assuming adult responsibilities. It's difficult to survive on your emotionally fulfilling but minimum wage job if you have a brood in diapers at home. Obviously you still have responsibilities, probably including property taxes, insurance, and utilities, if you own your house outright as opposed to having a mortgage.
BTW, it's a bit tricky to buy your home outright if you live, in, say Palo Alto, where I recall a bunch of YC-funded startups are based:
http://www.paloaltoonline.com/news/2013/12/24/real-estate-ma... "In Palo Alto the median sales price for a home was $2.2 million..."