Purse strings is a draw string used to close a handbag, or is slang for having control over the money.
When the wife is in charge of the money in the family and gives her husband an allowance, this is an example of when the wife has the purse strings.
a drawstring for closing certain purses
purse strings Idioms
hold the purse strings
to be in control of the money
tighten (or loosen) the purse strings
to make funds less (or more) readily available
Financial support or resources, or control over them: the politicians who control federal purse strings; tightened the corporate purse strings.