A preposition is a word used to show the relationship of a noun to something else, usually a location in space or time. A preposition is one type of a larger grammatical category referred to as adpositions. Virtually all adpositions in English are prepositions — with a few exceptions that can be used as postpositions, such as hence and thereafter.
In most languages, the set of prepositions is extremely subject to change, and English is no exception. Over time a word may take on meaning as a preposition, or may lose that meaning and no longer be classified as a preposition. For this reason, "complete" lists of prepositions in any language are a questionable affair, though many grammar textbooks still attempt to provide such a reference. When trying to determine whether a word is a preposition, one need only look to the role it serves in the sentence -- is it being used to demonstrate a spatial or temporal relationship between the subject and object of the sentence, or between two objects? If so, the word is likely a preposition.
Common prepositions include the words: about, above, after, among, around, at, before, behind, beneath, beside, between, by, down, from, in, into, like, near, of, off, on, out, over, through, to, up, upon, and with. This is only a sampling of the many, many prepositions found in English. Many prepositions are also formed by combining multiple words, such as the phrases ahead of, in front of, on top of, on to, and prior to. Additionally, many archaic prepositions are no longer in common usage, but still sometimes crop up in writing or speech, such as betwixt, versus, unto, and sans. A word such as but or except may be classified by some as a preposition, while others hold these words to be similar to prepositions, but not strictly belonging in that class.
In sentences such as four score and seven years ago or all evidence aside, we see examples of a different type of adposition, known as a postposition. English has few postpositions, and in most cases they may also be used prepositionally — we can change our example of aside in the above to be prepositional by simply changing the order, as in, aside from all evidence. A prepositional phrase is formed by combining a preposition with a noun and adding any additional modifiers that may be desired. In the phrase at work, for example, the word at is a preposition, and the noun work combines with it to make a prepositional phrase.
A prepositional phrase may serve a number of functions. It may be the object or subject of a sentence, or it may function as an adjective or adverb. In the sentence The women ran with vigor. for example, the prepositional phrase with vigor is acting as an adverb to modify ran. In the sentence The men are in denial. On the other hand, the prepositional phrase in denial serves as an adjective to modify the men.
There is some debate in English as to whether it is acceptable to distance the preposition in a sentence from its object, or to end a sentence with a preposition. Different grammarians have different feelings about these issues — though in most cases tensions run high. Usage recommendations seem to be tending towards the liberal as time passes, with few mainstream grammarians arguing against terminating a sentence with a preposition in a case such as This is something I can't put up with.