What is a chiasmus and what is its purpose?

A chiasmus is a literary technique where concepts or grammatical features are repeated but in reverse order. A simple way to remember it is A-B-B-A, just like the band!
For example: (Aeneid VI.102)
ut primum cessit furor et rabida ora quierunt (when first the frenzy quietens and the rabid mouths grow quiet) A B B A
In this case the two verbs are the 'A's and their subjects are the 'B's. There is a clear reverse order for effect, since the verb normally comes last in Latin. It is usually used to highlight or draw attention to the words that are the B's, here the 'frenzy' and the 'rabid mouths', important in the context of the poem.
It's a really useful construction to remember for the analysis questions about an author's writing technique!