Idiom; presumably of betting / gambling origin; talk is cheap; put up or shut up; don’t just say you think that horse is going to win, bet your money on it.
To put your money where your mouth is means to back up your words with actions. Instead of saying “Someone should really help those people” or “They need to re-paint that building” or “Public Radio should be better funded”, for instance, a person could take action; providing aid, re-painting, donating money.
There’s a rhythm to the idiom, because money and mouth are alliterative.
I remember a toothpaste commercial from the 1970s that played on this saying; the advertisers were suggesting that consumers literally spend their money on their mouths, on keeping their teeth clean.