Most divorce filings in the United States today are filed on "no-fault" grounds, and "irretrievable breakdown of the marriage" (or, in some states, "irreconcilable differences") is the most common phrasing for that standard. Encountering the term on a filing or a form is often the first time many people see it in writing.
What the phrase is doing
Before no-fault divorce became available nationwide, a spouse generally had to prove the other spouse did something specific, such as adultery, abandonment, or cruelty, to be granted a divorce. "Irretrievable breakdown" replaced that requirement in most states: it simply asserts that the marriage has broken down to the point that it cannot reasonably be preserved, without assigning blame to either spouse. In many states this is now the exclusive or dominant basis on which divorces are actually filed, even where older fault-based grounds technically remain on the books.
What it does not require
Filing on this basis generally does not require proving misconduct, presenting evidence of wrongdoing, or persuading a court that one spouse caused the marriage to end. Some states require both spouses to agree that the marriage is irretrievably broken for an uncontested filing, while others allow one spouse to assert it even if the other disagrees, sometimes after a required waiting or separation period.
Why the exact rule varies by state
Whether fault-based grounds still exist alongside the no-fault standard, whether both spouses must agree, what waiting period (if any) applies, and what a court needs to see before entering a decree all vary by state, and sometimes by county or court. This is exactly the kind of detail that can differ enough between jurisdictions that a general description is not a substitute for confirming the specific rule in the state and court where a case is or will be filed.
Where this fits into a filing
Seeing this phrase on a form is not a sign that anything unusual is happening. It is standard language in the large majority of cases filed today. A licensed attorney in the relevant state can confirm exactly what that state's version of the standard requires for a specific case.