What business is it of hers?
Sentences can be broken into Phrases. For example we have Noun Phrases, Verb Phrases, Adjective Phrases and so forth. Inside bigger phrases, we have smaller phrases. So, for example, we can break down the following sentence into different phrases:
- I usually eat square biscuits from France
- usually eat square biscuits from France
- square biscuits from France
- from France
The first example here is a special phrase called a sentence/clause. (2) is a Verb Phrase. Inside (2), we find (3) which is a Noun Phrase. (4) is a Prepositional Phrase.
The main grammatical word in each phrase is the head of the phrase. The head of the Verb phrase is the Verb, the head of the Noun phrase is the Noun. The head of the Preposition Phrase is a Preposition. Specifically the head of from France is the Preposition from. The main word there is from, not France.
Prepositions usually are followed by a Noun. In example (4), we see the preposition from followed by the Noun France. The complement of a preposition is the other words that belong to that preposition. So in "at the window", the complement of the preposition at is the window. In "from France", the complement of from is France. In the Original Poster's example the possessive hers is the complement of of in "of hers".
A Prepositional complement is another way of saying the complement of a preposition.
[It is a very unhelpful term though, because it could have two meanings ...
- the complement of a Preposition
- a complement which is a Preposition.
So, my advice is not to use this term yourself in your writing.]