The phrase to rob Peter to pay Paul, and its variants, mean:
– to take away from one person, cause, etc., in order to pay or confer something on another;
– to discharge one debt by incurring another.

This phrase occurs, for example, in Frayling warns government against backwards step in arts investment, by Jeremy Austin, published in The Stage (London, England) of Thursday 8^th July 2004:

Unless the government provides Arts Council England with a real term increase in funding, plus a further £20 million, clients face a return to the stop/start funding policies of the nineties, chairman Christopher Frayling has warned.
[…]
Frayling said that should government funding not be at the level he is suggesting, some of the ongoing capital projects—including work at The Lowry in Salford—would be affected.
“Special case Lottery projects, such as the Lowry, which are more than on the edge would need an infusion of money. Next spring, if we did not have £20 million, it will be at the expense of something else. If we don’t have an uplift, we will have to rob Peter to pay Paul.”

The phrase to rob Peter to pay Paul derives from the association of Peter and Paul, the names of two leading apostles and saints, and fellow martyrs at Rome. Additionally, like the names Jack and Jill, the names Peter and Paul alliterate and are both well known.

A similar phrase occurs also in French: déshabiller Pierre pour habiller Paul (i.e., to undress Peter to dress Paul). Randle Cotgrave recorded découvrir S. Pierre pour couvrir S. Paul (i.e., to uncover St. Peter to cover St. Paul) in A Dictionarie of the French and English Tongues (London: Printed by Adam Islip, 1611):

Descouvrir S. Pierre pour couvrir S. Paul. To borrow of Peter to pay Paule.

The names Peter and Paul occur in collocation with one another in the following passage from Lanfrank’s “Science of Cirurgie.” Edited from the Bodleian Ashmole MS. 1396 (ab. 1380 A.D.) and the British Museum Additional MS. 12,056 (ab. 1420 A.D.) by Robert v. Fleischhacker (London: Published for the Early English Text Society by Kegan Paul, Trench, Trübner & Co., 1894):

Sum medicyne is for peter þat is not good for poul, […] ffor if peter be of complexioun hoot & moist, & poulis complexioun be coold & drie, oon repercussioun * wole not serue hem boþe in oon point.

[* As a medical term, repercussion denotes the action of driving a morbid humour, fluid, etc., back to its source or away or inwards from a swollen or diseased part.]

The earliest occurrences of the phrase to rob Peter to pay Paul and variants are as follows, in chronological order:

1-: From Þe seven werkys of mercy bodyly (c.1382), by the English theologian and religious reformer John Wycliffe (c.1330-1384), as published in Select English Works of John Wyclif edited from original MSS. by Thomas Arnold (Oxford: Clarendon Press, 1871)—in the following passage, Wycliffe explains that alms are not pleasing to God if the money was not obtained righteously:

Siþ ȝyvynge is not worþe but if God approve it, but God approves not unjuste havynge of þinge, þanne it is non almes to dele of such catel. Lord, hou schulde God approve þat þou robbe Petur, and gif þis robbere to Poule in þe name of Crist?

2-: The phrase occurs on several occasions in Jacob’s Well, an Englisht treatise on the cleansing of man’s conscience. Edited from the unique MS. about 1440 A.D. in Salisbury Cathedral, by Dr. Arthur Brandeis (London: Published for the Early English Text Society, by Kegan Paul, Trench, Trübner & Co., Ltd., 1900)—for example, the following passage is about a rich man who confessed himself on his deathbed:

Cesarius seyth þat a ryche man of fals getyn good schrofe hym on his dede-bedde, wyth fułł sorwe of herte, to an holy Abbott, & sayde, ‘Abbot, ałł my good I ȝeue þe & to þin hows, þat þou & þi bretheryn pray for me, & answere for my soule.’ þe abbot seyde: ‘To robbe Petyr, & ȝeue it Poule, it were non almesse but gret synne. þe good þat þou hast falsly gett of oþere men, to wythholde it fro hem, & to ȝeue it to vs, it were dampnacyoun to þe, & gret synne to vs.’

The following folk-etymological explanation of the phrase to rob Peter to pay Paul is from The History of Edward the Sixth, Anno Regni Edw. Sexti 9. An. Dom. 1551, 1552, in Ecclesia Restaurata; or, The History of the Reformation of the Church of England (London: Printed for H. Twyford, J. Place, T. Basset, W. Palmer, 1670), by Peter Heylyn (1599-1662), Church of England clergyman and historian:

The Lands of Westminster so dilapidated by Bishop Thirlby, that there was almost nothing left to support the Dignity; for which good service, he had been preferred to the See of Norwich, in the year foregoing. Most of the Lands invaded by the Great men of the Court, the rest laid out for Reparation to the Church of St. Paul; pared almost to the very quick, in those days of Rapine. From hence first came that significant By-word (as is said by some) of Robbing Peter, to pay Paul.