Why and how was the Pastoral Provision created? First, how. In 1980 John Paul II responded favorably to a request made to him by a group of Anglicans that they might be received into full communion as a group, that their married clergymen might become Catholic priests, and that they might retain elements of their liturgical tradition.
Priestly celibacy is a discipline, not a doctrine of the Faith, and so it is dispensable, i.e. the requirement of celibacy may be waived in specific cases. By way of comparison, the Orthodox churches have always allowed married priests. They do not however allow priests to marry. Former Anglican clergymen who are already married may therefore become Catholic priests.
In regard to the liturgy, there are many different liturgical traditions within the Catholic Church and the Church is free to make adaptations as she sees fit. Just as the one Church has members who worship according to the Eastern Rite, and just as she revises the Western Rite (e.g. the liturgical reform of Vatican II), so she may allow the use of a revised Anglican liturgy.
Now, why was the Pastoral Provision created? Here one may not presume to know what the Holy Father was specifically thinking, but one may nonetheless speak with confidence about the general intent. The Pastoral Provision helps Anglicans who want to become Catholic to go ahead and become Catholic; it responds to this matter of conscience upon which it might otherwise be more difficult to act.
Most Anglican clergymen believe that they are already priests in the one holy catholic and apostolic Church, and so when they feel called to become Catholic, they feel they must either betray their ordination vows or simply accept that they never have been priests. While the latter is in fact the case (to put it bluntly), this is a difficult pill to swallow (even as much as one might know he needs the medicine). Compounding the difficulty is the need to support his family even after abandoning his profession. This practical reality alone might keep many men in their current positions regardless of their conflicted consciences. The Pastoral Provision is then a pastoral response to these men which allows them more readily to respond to the demands of conscience.
But this pastoral response helps in much broader ways was well. The former parishioners of these men will gain new clergymen who do not suffer from a conflicted conscience. They may thus see more clearly the distinctions between their own beliefs and the teachings of the Catholic Church. This is good ecumenism. Many of them may in turn decide to follow the example of their former clergymen and become Catholics themselves. This is good evangelism. Finally, these converts often become fully committed Catholics who do a great deal to build up the body of Christ; they have the converts’ zeal and knowledge. This is good catechism. In other words, by helping people respond to the demands of conscience, the Church does a positive good.
The Anglican liturgy approved for use by those who come from the Anglican tradition is simply more of the same. It helps people find their new home in the Church. It also preserves all that is good and true in the Anglican tradition and offers this for the benefit of the Church.