Prepositions are words that show the relationship between a noun or pronoun and other words in a sentence, such as "in," "on," "under," and "beside." Common prepositions include "at," "by," "for," "from," "of," "to," and "with," which are used to indicate location, time, and direction. Prepositions are essential for understanding and constructing meaningful sentences, as they provide crucial information about the relationship between different elements in a sentence.