Marital Property is property that a divorce court has jurisdiction to distribute between the spouses. Non-marital property is property of one of the parties only, and a divorce court cannot decide what to do with non-marital property: it is the property of it's owner, period. How to distinguish marital from nonmarital property?
Marital property is all property that is acquired from the moment of marriage until the end of the marriage, with the following exceptions: property acquired during the marriage as a gift, inheritance or by use of only non-marital property, that is not commingled. All property acquired during the marriage is presumed to be marital, so it is the burden of the party wanting to establish it as non-marital to demonstrate it falls into one of the exceptions.
Jointly titled property is commingled, and so it is marital. For example, a house that is jointly titled, or an account in both spouses' names is marital. Even if non-marital funds were used to acquire it, it is too commingled, and so too difficult to determine who owns what part of such an asset, so it is marital.
Property regardless of title, purchased during the marriage and not falling into one of the above exceptions is marital. A house in one party's name or a bank account in one party's name is marital. Typically, theses assets are acquired with the income of one of the party's. Income earned during the marriage is a result of "marital efforts", and the product of those efforts, wages/income is marital. What is bought with the marital income, is marital.
What about retirement assets? The answer depends on how those assets were funded. If, as is typically the case, the 401(k) or IRA was funded by contributions of the employer and employee during the marriage, it is marital. If the account preexisted the marriage, the part that existed at the time of marriage is non-marital, and the part that was contributed during the marriage is marital.
What if the asset is smaller than the attached debt, like an upside-down house? Well, the debt follows the asset, so if the house is marital, so is the loan. This result in a negative marital asset, or simply, a marital debt.
Some assets are easy to classify as marital versus non-marital. Other assets need to be traced to determine the source of funding before they can be classified as one or the other.
Even after an asset is determined to be marital or non-marital, how it should be divided can depend on how it was funded. For example, a house that is marital as a result of commingling a large non-marital contribution that enabled the purchase may be a candidate for a disproportionate distribution favoring the contributing spouse (say 70/30 versus 50/50). Consult with an experienced family law attorney.