It sounds like a made-up term, or a term for something that exists in a frat house only to be destroyed. But, a party wall is a real thing in the real estate industry, and are actually priority when pointing out features in an apartment or condo. A party wall is a shared wall that separates two separately rented or owned units, and are most often found in apartment, condo, or office complexes. In other words, it is a shared structure between two tenants. This does not always have to be a physical wall, but there are laws in individual states and cities that govern how a party wall must be constructed.
These “party walls” are sometimes built to add extra insulation between unites, and some building codes require them to be built with noncombustible material to act as fire walls. This is handy for diminishing noise between units, but more importantly, it will slow the spread of fire into conjoined units should one start.
There is also such thing as a “party wall agreement,” which establishes rules around ownership and maintenance for a shared wall. This functions to reach an agreement when disputes arise about the wall. Traditionally, each owner owns one half of the wall, and each owner is granted an easement for the support of the structure. These agreements can counsel all sorts of things, such as what tenants can hang on the shared wall and what consent must be given if there are structural changes. Once owners legally consent to the terms, party wall agreements are recorded in applicable land records. By including party wall agreements in public records, prospective buyers or renters can understand the property they are considering before agreeing to live there.