3 Answers

It is called the Caduceus.

There are many theories, the symbol was originally a Greek symbol of commerce (of all things!) and associated with the Greek God Hermes. In the seventh century, it was first linked to medicine as people used Hermetic astrological ideas based on planets. As you can see Hermetic comes directly from Hermes mentioned above.

Another idea is less pleasant, the treatment of Guinea Worm was to pull the worm out of the legs over a few days, wrapping it around a stick! The doctors would carry the stick and worm around to prove they were good!

It's popular today as the snakes are similar to a DNA double helix.

Search for "Caduceus" in Wikipedia for a full answer.

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http://ask.yahoo.com/20001109.html

1st Special Operations Medical Operations Squadron: Ultramarine blue and Air Force yellow are the Air Force colors.  Blue alludes to the sky, the primary theater of Air Force operations.  Yellow refers to the sun and the excellence required of Air Force personnel.  The dagger represents the AFSOC’s ability to deliver special operations capability globally through airpower.  The snake wrapped around the winged dagger resembles the caduceus and emphasizes the medical squadron’s role in AFSOC’s delivery of special operations capability.  The cross is the time-honored symbol of the combat medic.  The squadron motto emphasizes the commitment to the mission and the goal to keep the planes in the air, bringing the fight to the enemy.