Quasi in rem refers to a legal action which mainly involves property rights, but partly involves personal rights as well. A quasi in rem action determines the rights of a person in a thing. It deals with the rights of specific individuals in a thing, rather than the rights of the world in a thing.
For example, foreclosing a mortgage is a quasi in rem action because it seeks not to determine the rights of the world in a piece of property, but rather, the rights between the lender and the borrower. There might be others who could have interests too. Generally, a quasi in rem action tries to secure a preexisting claim in the property, or extinguish someone elses. In some cases, it may be used to substitute for personal jurisdiction, where a defendants property is applied to satisfy a claim that is unrelated to property.