Explanation (One True Faith)
Matrimony
See Catechism §§ 1601–1666. The Holy See’s text
What it is
Matrimony is the covenant by which a baptised man and a baptised woman give themselves to each other for life, for the good of the spouses and for the begetting and raising of children. Between the baptised it is a Sacrament. Christ is the one who binds it.
In Scripture
In the beginning God made them male and female and said that a man shall leave his father and mother and cleave to his wife, and they shall be two in one flesh. Our Lord quotes that sentence and adds, What therefore God hath joined together, let no man put asunder. Paul calls the union of husband and wife a great mystery, in reference to Christ and the Church.
What the Church teaches
The spouses are the ministers. The Priest or Deacon assists and blesses in the name of the Church. For a Catholic, the marriage must ordinarily be contracted before the Church’s witness, or it is not valid. Consent must be free, and there must be no impediment. The bond is exclusive, faithful, and open to life.
See Catechism §§ 1601–1666.
How it is celebrated
The couple declare their consent in words the Church can hear. They give rings. The nuptial blessing is prayed. If both are Catholic and the Mass is celebrated, they may receive Communion, being in a state of grace. A wedding is not a Mass by necessity. It is a Sacrament by the consent of two baptised people, rightly given.
What it does
The Sacrament gives the grace to love as Christ loved, which is a daily thing and not a feeling at the altar. It makes the home a place where children can be taught the Faith. A civil divorce does not dissolve a sacramental bond. A declaration of nullity, when a tribunal finds that a marriage never validly existed, is a judgement about the beginning, not a Catholic form of divorce.
If this is your question
The hard cases belong in a Parish and, if needed, a tribunal. They do not belong in a slogan. If you are living in a second union and cannot receive Communion, you are not cast out of the church building. Speak to a Priest. Do not decide your own canon law from a comment online.