OK, here is the truth of Catholic annulment:
Catholics believe that matrimony is a sacrament, like baptism. In the same way that you cannot be "un-baptised", you cannot be "un-married". Once it's done, it's done.
However- the Catholic Church has a number of requirements for the sacrament(s) to be considered valid- i.e. form (how the sacrament is administered), etc. For example, you cannot receive the Sacrament of Reconciliation (Confession) until you have reached the age of reason.
There are several requirements for the Sacrament of Matrimony, including age, ability to consent freely, intention to be open to children, intention to remain faithful, ability to understand the duties and responsibilities of marriage, etc.
When the Church grants an a annulment, they are NOT saying that the marriage never took place, or that the children are illegitimate. They are saying that the marriage did not rise to the level of a Sacrament, and that the Sacrament (NOT the marriage) is declared null- or invalid.
An annulment inquiry does not take into account what happened after the wedding day- in other words, if you married with the intention of remaining faithful and then 15 years later had an affair- that does not automatically mean an annulment. The Tribunal is only concerned with the state of mind and intentions of the couple on the day the Sacrament was administered (the wedding day). Because the Sacrament itself is what is in question, not what happened after that. However, if a couple gets married, and on the wedding day one of them is actively involved in a sexual relationship with another person- that is evidence of a lack of intention to remain faithful within the marriage and constitutes an impediment to the Sacrament.
The Catholic Church believes that any person is able to enter in to a Sacramental marriage, even if they are not married in the Church, or indeed, even if they are not Catholic. Any baptized person is considered to have a Sacramental marriage unless proven otherwise. That is why the Church requires non-Catholics to go through the annulment process in order to be married in the Catholic Church.
Marrying after a civil divorce and without a Declaration of Nullity is considered adultery, which is a mortal sin. When you are granted an annulment you are free to receive the Sacrament of Matrimony because it has been determined that you have not received it previously. Just like with baptism, you cannot be "re-baptized"- and you cannot be "re-married". You can't receive a Sacrament twice.
There is A LOT of misinformation floating around about what an annulment is and what it isn't, the reasons why they are granted or denied, and what the rules are for marrying again in the Church. Please check with the diocesan Tribunal office in your area for the accurate answers. Not all priests know the finer points of canon law.
As for Pope Francis, he is not saying anything that is particularly new or different- he is just saying it in a new way:
Civil divorce is NOT a sin in the Catholic Church, and it never was. Divorced Catholics are still considered Sacramentally married until the previous marriage is annulled. They may receive communion as long as they are not in a sexual relationship with another person or remarried without an annulment. (Both of those things would be considered adultery against the first marriage until an annulment is granted). Catholics are welcome to receive Communion as long as they are not in a state of mortal sin (adultery is a mortal sin).
So... divorced, un-annulled Catholics who are not sleeping with anyone else or remarried to anyone else are considered in good standing with the Church and can receive other Sacraments (Communion is a Sacrament).
Un-annulled Catholics who are re-married will never be openly allowed to receive Communion or other Sacraments because they would be considered in a state of mortal sin, and Catholic law says that receiving Communion in a state of mortal sin is another mortal sin. Priests are within their rights as guardians of the faithful to refuse Communion to a person in a known state of current mortal sin. They cannot knowingly allow someone to commit a sin that could cause them to go to hell.
The Church would have to change the rule about receiving Communion in a state of mortal sin, which they will not do.
And yes, I have received an annulment of my previous marriage. The process was not intrusive or insensitive, but it was not easy. Any questions?
[This message edited by Eranda at 10:08 AM, April 27th (Sunday)]