To expand on Affable's answer, the entire book of Mark is one chiasmus made up of many fractally layered chiastic structures. The center of the Mark "sandwich" is:
And he asked them, “But who do you say that I am?” Peter answered him, “You are the Christ.”—Mark 8:29 (ESV)
The layer just outside of that center illustrates the two misconceptions about who Jesus is:
And Jesus went on with his disciples to the villages of Caesarea Philippi. And on the way he asked his disciples, “Who do people say that I am?” And they told him, “John the Baptist; and others say, Elijah; and others, one of the prophets.”—Mark 8:27-28 (ESV)
And he began to teach them that the Son of Man must suffer many things and be rejected by the elders and the chief priests and the scribes and be killed, and after three days rise again. And he said this plainly. And Peter took him aside and began to rebuke him. But turning and seeing his disciples, he rebuked Peter and said, “Get behind me, Satan! For you are not setting your mind on the things of God, but on the things of man.”—Mark 8:31-33 (ESV)
Everything before Peter's confession points to Jesus' identity as the Christ and everything after points to the need for the Christ to suffer, die and be resurrected in order to accomplish his mission. Mark's structure is so magnificently constructed that it's utterly clear that the endings some manuscripts contain are superfluous. Mark begins with a single witness to Christ Jesus and ends with the possibility that the witnesses to His Resurrection will fail to pass on the message because of fear. Mark 1:1 might be a scribal insertion as well.
The message is in the center
Key to understanding the chiastic structure is to notice that the meaning is the meat in the center of the sandwich. One purpose of the structure is to draw the reader (or listener) into peeling back the layers of story to get to the core lesson. Authors often use the contrast between the bread and the meat to draw out some important distinction. Finding out what the author meant can be a bit of a puzzle.
The Jairus' daughter/hemorrhagic woman periscope illustrates chiastic contrast well. There are obvious differences between the outer and inner layers:
Age: 12-years old | 12 years of bleeding
Urgency: near death | chronic condition
Station: daughter of a ruler | a widow
Community: many "mourners" | a lone woman
Situation: private room | crowded street
Healing: spoken words | a touch
There are certainly even more contrasts, many of which can't be expressed in a few words. Ultimately, I think the core message is that Jesus isn't too concerned if you do everything by the book (as Jairus did) or if your life is a total mess (as the woman's was). Each got the same healing from Jesus.
Mark's account seems to have left out many of the iconic details of Jesus' life in order to maintain a consistent structure. We don't have a Christmas story because, I suspect, it would have interfered with the central message. The chiasmus is Mark's signature; his gospel is marked with a χ. Luke is more careful with his sources, Matthew is more tuned into Jewish culture, and John seems to come at Jesus' biography from a completely unique angle. Their handling of this story turns out to be a great case study.