What is a preposition and what does it modify?

A preposition is a word or group of words that combines with a noun or pronoun to form a phrase.
A preposition alone does not modify.
However, when it is combined with a noun or pronoun to form a prepositional phrase, the phrase can act as adjective (modifying a noun/pronoun), or adverb (modifying a verb, an adjective, or another adverb).
A prepositional phrase can also act as a noun.
Examples:

The child ran across the street.
The preposition “across” does not modify anything.
However, the prepositional phrase “across the street” acts as adverb to the action “ran”.
Ask: Where did the child run?
Ans: across the street

The man beside my aunt is my uncle.
The preposition “beside” does not modify anything.
However, the prepositional phrase “beside my aunt” acts as adjective modifying the noun “man”.
Ask: which man?
Ans: man “beside my aunt”