What a decree of Nullity Is. An annulment, properly called a Decree of Nullity, is a finding by a Church tribunal that ON THE DAY VOWS WERE EXCHANGED at least some essential element for a valid marriage was lacking, such as, one of the parties did not intend lifelong fidelity to the other person or excluded children entirely. Another example would be that one of the parties was incapable of marriage (due to some constitutional weakness, such as mental illness or some psychological condition that prevented making the marital commitment - gross immaturity, homosexuality, etc.).
None of these conditions are assumed they must be proven. A Decree of Nullity does NOT dissolve the marriage, it cannot. It is a reasoned judgement that one never existed, and as such is capable of human error. If the tribunal is fastidious to Church law and theology and the couple and their witnesses are honest, the decision can be followed in good-faith, including a new marriage. If someone is ABUSING the process through deceit, however, it would be a very grave sin for that person. A person who innocently enters a second marriage would not be guilty of sin, but the person who abused the process to fraudulently obtain a decree in order to remarry would commit adultery by remarrying.
An "annulment" does NOT concern whether the marriage was a happy one, whether one of the spouses LATER became unfaithful, or LATER decided not to have children, but only their INTENTION on the wedding day. If a marriage was made THAT day it is a life-long bond, irrespective of what happened later in the marriage. To "annul" a marriage based on "failure to achieve communion" or some other factor not recognized by the Holy See (as has been done) is not a decree of nullity at all but a divorce. Such decisions are a source of grave scandal in the Church and are both canonically and morally invalid.