What is a Declaration of Nullity, what many improperly call an Annulment?
The Catechism of the Catholic Church on Marriage and Nullity, with references to the Code of Canon Law:
1628 The consent must be an act of the will of each of the contracting parties, free of coercion or grave external fear. (Cf. can. 1103) No human power can substitute for this consent. (Cf. can. 1057 #1) If this freedom is lacking the marriage is invalid.
1629 For this reason (or for other reasons that render the marriage null and void) the Church, after an examination of the situation by the competent ecclesiastical tribunal, can declare the nullity of a marriage, i.e., that the marriage never existed. (Cf. can. 1095-1107) In this case the contracting parties are free to marry, provided the natural obligations of a previous union are discharged.