It's an idiom. It means her parents had foolishly spent all of her money. For example, instead of saving it or investing it, they may have spent it on gambling, fancy cars, designer clothes, and lavish trips --things that don't increase in value.
OTHER EXAMPLES:
"He blew all his money at the racetrack," meaning he bet all of his money on horses that didn't win.
"I really want this job, but I don't think I'll get it because I blew the interview," meaning he didn't do well at the interview.
"He blew his top," meaning he got very angry.
"He says he's going to sue me, but he's just blowing smoke," meaning he is talking tough, but he's not going to follow through with filing a lawsuit.
"She gave the police information that blew the case wide open," meaning the information she provided was so dramatic and explosive that the police were able to solve the case.
"I tried to talk to him about my problem, but he blew me off," meaning he didn't take me seriously and he is not going to take any action to resolve the issue.
"We had a dinner date, but he blew me off," meaning he didn't show up for the date.
"I saw her at the party, but she totally blew me off," meaning she ignored me.
As you can see "blow" is used in many phrases and can have many meanings, but please be careful. I'm American, and in the U.S., "blow" is also used to describe a sexual act. "Blowing someone off" and "blowing someone" are two VERY different things.