The Bible is full of chiasms (kai'-a-zumz), literary structures used to provide a framework to a story--what a novelist might call a story arc--or to convey additional meaning to what is contained by the bare text. The singular is chiasm and the plural is sometimes given as chiasmi, since the word is derived from Latin. In a chiasm, a series of phrases or concepts in the first half of the narrative are mirrored in the second half, usually--but not always--with one, unmirrored statement at the center.
Chiasms were used extensively by writers in many ancient cultures, and sometimes they are still used today, especially in poetry and song. Along with parallelisms, thematic allusions, Hebrew word play, and a number of other literary devices, chiasms can give fascinating insight on the meaning that the original Biblical writers intended to convey. They can be as short as a single verse or span multiple books. Most commonly they span a few verses or a chapter.
A typical chiasm might look something like this:
A - God speaks to prophet
B - Prophet speaks to people
C - People respond to man
D - God acts
C - People respond to God
B - People speak to prophet
A - Prophet speaks to God
Sometimes they are very easy to see, but often they are obscured by translation from Hebrew or by artificial chapter and verse divisions. Being able to read the Hebrew (which I cannot), definitely makes them easier to find. Tony Robinson has a lot of great teaching on chiasms and thematic connections in Scripture. You can check them out here: Restoration of Torah Ministries.
And I have a growing list of them here: Index of Biblical Chiasmi and Parallelisms.