As was explained in a golden age issue, Wonder Woman once while trapped in space squeezed the earrings with her super strength, thus freeing enough oxygen (as she broke the chemical bonds) with which she could breathe. They were later re-explained as having this ability as a magical property.
This was an ability mostly forgotten towards the end of the silver and bronze ages of comics, and with the 1980s George Perez reboot they returned to purely decorative in nature. They are often shown as either large bulbous circles or as stars. In her new costume in the DC reboot (the new 52) she no longer has earrings.
Alternately, for a brief period in the 1970s during the two years or so when she was depowered she wore earrings which had doubled as miniature grenades. These were powerful enough to blast her way past a steel door. They were fashioned by a reformed demolitions expert who Wonder Woman had previously captured (though the first time he was shown was after he had created the earrings.) Despite this new development for the character, the earrings were used only once, and soon Wonder Woman reverted to her original costume as well.