Chiasmus is when you say something like, for instance:
I adore Belinda,
and then, to emphasise the fact, you say it again, only sort of backwards:
she is my darling.
As you can see, it's not that the words are in reverse order, it's that the thing that was at the end of the phrase is now at the beginning, and vice versa.
As a classier example, the second line of this speech of Othello's is a chiasmus:
But O, what damnéd minutes tell he o'er
Do chiasmi matter? Well, they're a useful way of emphasising something, so if you're trying to be persuasive it might be worth bearing in mind.
Mind you, if you're trying to be persuasive there'll probably be about a hundred more important things on your mind.
So chiasmus is probably mostly a way of trying to make yourself look clever.
Thing To Consider Today: chiasmus. This word is from the Greek khiasmos, a cross-cross shape. Chi is the Greek name for the letter X.