Spooky - I was thinking about this idiom only this morning!
It means risk your own money to support what you say. Often it's used to invite people to make a bet: 'I think Lacy Lady will win the 2.30.'/'OK, if you're so sure, put your money where your mouth is'. In the example you give, the banks will only support a business venture if they believe the client is prepared to risk his own money; typically, a bank requires a client to use his/her own property as collateral for a loan.