Prepositions are linking words that are put before nouns and pronouns, and describe something's location or other information. In the sentence "The cat sits on the sofa", the word "on" is the preposition.
The entire purpose of language is to communicate. Prepositions make our communications much more precise. So if your teacher wanted you to bring him a piece of paper from his desk, he might describe it thus: "handwritten", "unlined green paper", "crumpled". He might also describe its position: "in the middle of the desk, near the lamp, on my copy of Macbeth, possibly under my lunch." Here the words "in", "near", "on" and "under" are the prepositions telling you exactly where to find the paper.
A preposition must be attached in some way to a noun: "in the middle of the desk, near the lamp, on my copy of Macbeth, possibly under my lunch." Now you can see how each of the prepositions is followed by a noun (or noun phrase) in bold. Use prepositions to make your writing more precise.
To hone your preposition skills, play this quiz on the subject.