Annulment means the ability of a court to find a marriage to be void or voidable. If you are already married to person A and you go out and get a marriage license and try to get married to person B, that is bigamy. It is a crime, for one thing, but more importantly, for the purposes of this analysis, you can not be married to person B if you are already married to person A. Thus the marriage to person B is void, meaning it never took place. You may have a marriage license with the name on it, and you may have solemnized that with a minister, but that marriage is a void marriage.
If you need paperwork or documentation for an insurance carrier or for some other reason declaring that second marriage to be void, the court could annul that second marriage and state in a court order that it is void. But it is void from the beginning. According to VeryWellMind, there is a distinction there because there are other situations in which a person could get married and the marriage order itself could be voidable.
There are reasons why annulment could happen. One of the parties might have a lack of mental capacity to enter into marriage. A court could look at that as a factual determination. It will have to hear evidence on that issue and make a determination as to whether the person actually did not have the mental capacity to enter into marriage and did not understand what marriage was. This could be a person that has a diminished IQ or some other mental health issue that lets them not understand what they were entering into.