Prepositional complement is the name given to the noun or noun phrase that follows a preposition, such as "in town", "at work", or "the pen of my aunt". This is a logical development of the idea that a complement is something which completes something. In this case, a preposition, whose function is to show the connection of a noun or noun phrase to the piece of language in which it is used, needs a complement.
In older grammars, this idea was expressed by saying that a preposition governs a noun. 'Govern' here means (of a preposition) "to require (a noun or pronoun) to be in a certain case" (OED). This derives from the study of Classical languages, where case was far more important than it is in English. Prepositions in Latin demanded that a noun be inflected for a particular case, and different prepositions demanded different cases: commonly the accusative or ablative, less often the dative. Some prepositions even meant different things according to the case used in the noun: those that had a general meaning of place, like in, had a static meaning with the ablative case (English 'in'), but a sense of movement with the accusative case (English: 'into').
You may still hear - though it is not common these days - a reader complain about a writer, "Doesn't (s)he know that a pronoun governed by a preposition should be in the accusative?" For an explanation, see agreement of preposition with pronoun.