A marriage dissolution is more commonly referred to simply as a divorce, and refers to the situation where a marriage is ended, breaking the legal bond between the two parties and resolving any outstanding disputes that have arisen in the process. Marriage dissolution may be induced either by one of the parties in the marriage, or mutually by both, but statistically it's more common for a marriage to be ended by demand of one of the parties. In such cases, the property separation is decided by authorities and settled in a legal court case, with both parties usually hiring lawyers to represent them in the case and defend their interests as best as possible.
It should be noted that a marriage dissolution is different than an annulment, in which case the marriage is declared null and void retroactively, that is, from the very beginning of the marriage - and there are different legal proceedings attached to an annulment as opposed to a regular divorce. Some jurisdictions prevent marriage dissolution entirely, while others have some harsh and strict laws related to the division of property, which end up being exploited by malicious individuals in some notorious cases.
There are some special cases related to a marriage dissolution, for example the so called "summary divorce", which occurs when the marriage has been going on for a short period of time with a small amount of property to divide between the two parties and no children involved. This type of divorce involves faster legal proceedings than regular divorces do.