The meaning of the phrase "Money doesn't grow on trees" means that money cannot simply be plucked from a tree the same way you pluck a leaf from a tree or a pedal from a rose. Money is something you have to make or earn.
To turn a tree into a money, you have to cut the tree down, grind it up into chips, boil the chips, and flatten the boiled mixture, dry it and cut it up into paper. Then you have to print the ink for the bill template onto the paper, incorporate anti-counterfeiting measures, and cut the bill from the larger roll of paper before the paper can be called money.