Public money is the amount of money the majority of people are betting on a certain side.
It's as simple as it sounds. For example, if 75% of the bets are on the Chiefs -7 against the Rams, the public money is on the Chiefs.
This is important because the public is wrong more often than not, which is why sports betting exists. Public money is in reference to the bet percentage, which is different than the money percentage. In the above example, maybe only 25% of the money is on the Chiefs. This means that while there are more bets on the Chiefs, there are bigger bets on the Rams.
In that extreme case, it's likely due to the sharps (pro bettors), who are dumping money onto the Rams +7 because they see an advantage in the line. It's not always that extreme, but it's rarely a good idea to back where public money is going, especially if it's more than 80%. This is usually called fading the public.