A prepositional phrase may be:

1. a complement — which adds modifying (necessary) information to complete the meaning of the clause — it modifies a noun or a verb with information such as timing, location, or manner. A prepositional phrase is typically short and may include another prepositional phrase. The preposition is usually followed by a noun phrase : We began in the morning.  Our walk in the morning on the beach is refreshing.  The preposition may include the noun: We exercise indoors. See Preposition Uses.
2. an adjunct — which adds modifying (extra, unnecessary) information before or after the clause — it modifies the clause with information such as reason, purpose, condition, comparison, or relative timing. A connective prepositional phrase is longer. The preposition is followed by a finite clause (a full clause), a nonfinite clause (a gerund clause), a noun phrase or a prepositional phrase:  We began walking because we needed exercise. We began walking because of our health. We began walking after eating. We began walking after breakfast.  (Note that the main clause can stand on its own without the adjunct prepositional phrase.)

The head preposition of a phrase:

• is the primary word of the prepositional phrase.  It is called a head because of (1) its beginning (initial) position in the phrase → We walk [because we like fresh air] or (2) its role (meaning) in the phrase → We walk [because (reason) we like fresh air.  In the case of a double preposition, it is the first preposition that is the head.  We walk inside of the park.  We can't get out of the house early enough.
• functions as the connector between the main clause and the phrase. It also relates the information in the phrase to the central idea of the main clause. 
• relates a phrase expressing a meaning of: reason (because, since, as), concession (though, despite), purpose (in order, so that), time-relative (after, before, when, while, until), condition (if , unless), an expression (in a flash), comparison (than, as, of, from or to) and more.
• takes form as:
  • a preposition—before, after, while, because, though, until, as, than, if , and so on—may take a complement of a noun phrase, a gerund, an infinitive, a full clause or another structure, depending on the meaning of the preposition: before midnight (N), before the midnight hour (NP), before leaving home (Ger), He prefers to leave early rather than to leave late (Infin), before we left home (clause). 
  • a comparative preposition—as, than, of, from or to—followed by a full or reduced clause. He walks as fast as I walk. He walks faster than I do. He walks the fastest of us all. He walks a different route from the one we walk. His route is similar to our route.) 
  • a conditional preposition—if or unless— followed by a clause expressing a condition. We walk [if we have time].

How does a connective preposition differ from a coordinator (and, but, or) or subordinator (that, if, whether)?

• the head preposition is part of (holds meaning in) the phrase that it adds. It cannot be omitted without a loss of meaning → She is tired [because she walks.] 
  • a subordinator (that) is not part of the clause that it joins, rather it is a marker before the subordinated clause. That can often be omitted. → She says [that] she likes walking. If and whether are not omitted. (I don't know [whether] she actually does.)
  • a coordinator (and +, but–, or+/-) is not a part of either clause that it joins and has little (minimal) meaning. It can usually be omitted. → (She likes to walk; he does too. She wears running shoes; he wears track shoes.) The relationship of the clauses can be understood from context. Or is not omitted. (Do your best [or] go home.)
• the meaning expressed by the preposition can usually be modified by an adverb such as [1] a focusing adverb (He walks only because his health requires it.) or [2] a degree adverb (He walks partly for his health. He walks right in the middle of the path.)
  • a subordinator carries no meaning within the clause, so it does not accept a modifier: It is clear to us *exactly that he needs help.
  • a coordinator (and +, but -) carries limited meaning, so it does not accept a modifier (We walk in the morning *exactly and talk about plans.) Read more about Properties of Prepositions, Properties of Coordinators, Properties of Subordinators.

Also see other clausal heads—who, when, where, why—(interrogative pronouns) that occur in embedded wh-questions. Similar to other phrasal heads, the head of the clause is the connective, and it carries meaning as part of the clause. She told me who is coming. She told me whom she invited__.  (An object pronoun is moved to the beginning (head) of the clause.)

"Preposition"

The Cambridge Grammar of the English Language (2002) included some major changes to the category of Preposition. At first look, the recategorization of several adverbs and conjunctions as prepositions upsets what we thought we knew about prepositions. However, on closer examination, the recategorization makes a lot of sense. Linguistic research has produced (1) a description of English that is more logical and concise than the traditional Latin-based grammar we were using; (2) terms that can be applied globally to all languages (i.e., a word categorized [defined by properties] as Preposition in English will function in the same way as words called Preposition in other languages.)

1. One result is that the category Preposition has been widened to include words such as—before after, while, because, though, if, than, and as. Linguistic analysis determined that these words functioned more similarly to prepositions than to conjunctions, adverbs or other categories in which they had previously been placed.
2. Another result is that prepositional complements (structures that can follow prepositions) have been widened. A preposition is not limited to a noun as its "object". The complement of a preposition could be a word, phrase or clause—at home (N), in the house (NP), out of the house (PP), in stead of later (Adv), after leaving (gerund), because we left (clause). See Prepositions–Range of Complements.

This Connective is also called an adverbial preposition. The structure is called an adjunct prepositional phrase (linguistic description) or an adverbial clause (traditional term). See Connector Overview: Grammar Notes for grammar source details.