What does it mean to grant a church to a priory?

The quick answer (If there is one) is that Simon didn't control those churches(which were essentially the homes/estates of secular canons), he just set aside and funded the construction of the new home (Newenham) for the existing secular canons which were already associated with the church of St. Paul's.

This was taking place as a conversion of secular to regular canons agreed upon by both the church and the monarchy, due to some controversy at the time.

From A brief History of St. Paul's

The conduct of the clergy in Bedford does not seem to have been as exemplary as it ought to have been, however, and in 1164 one of their number, Philip de Broy, killed a man, and, whatever the circumstances were, it damaged the good name of the canons of St Paul's. This situation was not uncommon in other towns at the time, and in order to avoid such incidents several other collegiate foundations had adopted the practice of housing such clerics together in priories following the Rule of St Augustine.

This was seen as a satisfactory solution for Bedford, and the countess of Bedford Castle, Rose de Beauchamp, and her son Simon, found a suitable site just outside the town. In 1165 at a service in St Paul's, Simon confirmed that all the canons prebends and possessions be transferred to a spot about a mile downstream of Bedford, which they named "Newenham" or "new home" - now known as Newnham.

This essentially converted the secular canons of the collegiate church to regular canons of the Augustine priory. The wiki article on canons clarifies the difference somewhat:

Originally, a canon was a cleric living with others in a clergy house or, later, in one of the houses within the precinct of or close to a cathedral or other major church and conducting his life according to the customary discipline or rules of the church. This way of life grew common (and is first documented) in the eighth century. In the eleventh century, some churches required clergy thus living together to adopt the rule first proposed by Saint Augustine that they renounce private wealth. Those who embraced this change were known as Augustinians or Canons Regular, whilst those who did not were known as secular canons.

The History of the County of Bedford discusses the establishment of the Priory, and the assets it controlled (emphasis mine):

The original endowment of the priory by Simon de Beauchamp comprised the tithes of fourteen churches—St. Paul's Bedford, Renhold, Ravensden, Great Barford, Willington, Cardington, Southill, (fn. 34) Hatley, Wootton, Stagsden, Lower Gravenhurst, Aspley, Salford, Goldington; portions of land in many places which had belonged to the old canons; the tithes of all his markets, assarts and woods; the castle mill and another with some lands and water attached; the free use of all waters belonging to the castle, as far as Fenlake, for fishing, navigation and breeding swans; and the right to pasture a certain number of cattle with his own free of cost. These gifts are rehearsed with much detail and some additions in the Great Charter of William de Beauchamp. At the time of the Taxatio the income of the priory appears as £164 10s. 8d., (fn. 35) of which £92 6s. 8d. is made up of spiritualities. The largest items amongst the temporalities are lands, etc., at Goldington, Salpho, Stotfold and Sharnbrook; (fn. 36) and these are found in the Feudal Aids as portions of knights' fees.

This information is repeated in the book Money and the Church in Medieval Europe, 1000-1200: Practice, Morality and Thought

...the estates of the pre-existing secular canons were transferred to the new house, along with the tithes of 14 churches in Bedfordshire...

So this clarifies the issue and the distinction between the two groups of 'churches' mentioned. Those that were in the possession of the secular canons went with them into the priory, to be absorbed (depending on each of those original deeds) into the priory's funds when these canons passed. This is mentioned directly in another source, The Schools of Medieval England, by Arthur Leach:

the Norman lord Simon Beauchamp founded in Bedford an Augustinian priory and provided that as the secular canons of St Paul's died off they were to be replaced by regular canons and granted the church to them One of the secular canons was Nicholas also Archdeacon of Bedford and Canon of Lincoln About 1155 he executed a deed clearly under compulsion addressed to 'all the sons of holy mother church' Know ye all that St Mary's chapel with the tithes of Hordelhide and Bedford school scolas Bed which I have held for some time with the consent of my fellow canons I confess to be of the right of and appurtenant to St Paul's church and therefore I have voluntarily resigned them to Auger the Prior and the convent of canons regular of that church The priory having acquired the church and school was afterwards moved outside the town down the river to Newenham and became known as Newnham Priory Not till after the dissolution of monasteries did the school escape from the control of the regulars when it was refounded by the corporation under a charter of Edward VI and re endowed by William Harper ex Lord Mayor of London under Queen Elizabeth

Another document from the same Cartulary provides insight into the others involved in this decision/transaction; the authority by which these transfers were made.

Charter document 7 from the Deeds collection of the University of Toronto

Simon de Bellocampo omnibus fidelibus sancte ecclesie salutem Notum sit vobis quod ego Symon de Bellocampo dedi et firmiter concessi ecclesiam sancti Pauli Bed[] cum omnibus prebendis et possessionibus eidem ecclesie pertinentibus ad religionem in manus Willelmi primi prioris ibidem canonice constituti et in manus omnium successorum eius professionem religionis tenencium pro salute anime mee et pro anima patris mei et omnium antecessorum meorum qui supradictas prebendas de suis elemosinis ad seruiendum deo fecerunt et pro salute anime matris mee comitisse Rohesie et fratrum meorum et omnium parentum meorum Si vero prior decesserit electione conuentus et meo assensu alius prior substituatur Hanc donacionem confirmari feci auctoritate apostolica et domini mei Henrici regis Angl[] assensu et confirmacione annuentibus Thoma archiepiscopo Cant[] et Roberto Linc[] episcopo Hec autem donacio sollempniter facta est in supradicta ecclesia sancti Pauli astante clero et populo Huius donacionis et confirmacionis mee sunt testes Albricus comes auunculus meus Willelmus comes frater meus Rogerus Bigod Gilbertus de Ver[] Galfridus Loring[] Paganus filius Brien Radulphus de Berner[] Walterus de Mand[] Hosbertus filius Ricardi Reginaldus de Auco Willelmus de Bouill[] Johannes de Rochell[] Robertus de sancto Quintino Radulphus Folenfaunt Rogerus filius Huberti Radulphus clericus

this roughly translates:

Simon de Beauchamp, to all the faithful of the holy church, let it be known to you that I gave and firmly granted the church of St. Paul Bede, with all prebends and possessions belonging to that church, into the hands of William the first prior, canonically placed there and in the hands of all his successors. a profession of religion that hold fast for the safety of my soul and for the soul of my father and of all my ancestors who have made the above-mentioned prebends of their alms to serve God another prior to be substituted I made this gift to be confirmed by the apostolic authority of my lord Henry king of England and with the assent and assent of Archbishop Thomas of Cant and Robert Linc Bishop Witnesses to my confirmation are Earl Aubrey, my uncle William, Earl my brother Roger Bigod, Gilbert de Ver, Geoffrey Loring Payne, Ralph de Berner, Walter de Mand, Hosbert son of Richard, Reginald de Auco, William de Bouill, John de Rochell [] Robert of St. Quintinus, Ralph of Folenfaunt, Roger the son of Hubert, Ralph, clerk

We can see that this transaction was not just by Simons authority alone, but listed Bishop, Archbishop and King as backing the deal...

(Its worth noting also that this archbishop mentioned was Thomas Becket, and that Simon Beauchamp is listed as one of the signers of the Constitutions of Clarendon in 1164)

An explanation of the term prebend, and its relationship to the secular canons may help clarify this issue as well:

At the time of the Domesday Book in 1086, the canons and dignitaries of the cathedrals of England were supported by the produce and other profits from the cathedral estates.3 In the early 12th century, the endowed prebend was developed as an institution, in possession of which a cathedral official had a fixed and independent income. This made the cathedral canons independent of the bishop, and created posts that attracted the younger sons of the nobility.

So by by creating a powerful priory such as this, the Church consolidated its wealth and control, while the Monarchy removed a loophole through which lesser nobles were removing lands from the kings control and essentially providing inheritance to younger sons by establishing them as secular canons.

No more 'loose canons' so to speak.