An abstract of judgment is exactly what it sounds like. It is a written form of judgment between two parties that states who owes who. It gives details like how much interest must be paid, rules the loser must abide by, how much court costs, and so forth. This will be filed with the county of record, and used to have it on public record if the debtor (the person owing) is not abiding by the judgment.
There are a number of problems associated with these judgments, because a debtor may have a number of other debts on file as well. Any abstract of judgments, secured loans, or federal debts will take precedence over your claim. Additionally, the debtor may move to another county, or file bankruptcy to try and avoid the debt.
In many cases, if a debtor purchases a home, or a car, or any liquid (that is, something that can be sold or cashed in) item in the future, then the sheriff of that county can force the debtor to do so, and pay the person owed in the abstract of judgment on file. This is an arduous process, and virtually impossible if you do not have this abstract of judgment on file.
This is also a very important document for the debtor, as it contains all the important information of what is required of him/her.