Phrase that came about after The Great Fire of London which occurred on September 2, 1666. Money was taken from the coffers of St. Peter's Church to pay for repairs to the larger St. Paul's Church.

The phrase indicates leaving something undone, in order to do something else.

Using the rent money to pay the phone bill, not going to visit your mother, so that you can spend time with your SO, giving a gift you bought for a friend to your sister, when you suddenly remember her birthday, are all examples of "robbing Peter to pay Paul"

The intimation is that you should really be doing both things, not only one.