It's a palm branch, often a symbol of victory and triumph, but as the poster is inspired by the play, I guess you'd have to read the play to know exactly what Mucha and the playwright had in mind in this case. Wikipedia says "the palm tree was a sacred sign of Apollo in Ancient Greece because he had been born under one in Delos", and as Gismonda was a Greek melodrama, maybe that's it. In any case, it's almost certainly also intended to put Sarah Bernhardt herself on a pedestal:
"The basis of the motif was the solemn procession scene from the final act of the play, which also determined the stylistic conception of the poster: the sumptuous, priestly-vestment-like costume, the symbolic palm-frond and the mosaic-like background with its hint of a halo all suggest a sacred atmosphere, reflecting not least the veneration of the actress as a cult figure, the muse of the belle epoque."
Sources and suggested reading:
http://www.all-art.org/symbolism/mucha2.html
http://en.wikipedia.o.../Palm_branch_(symbol)
http://en.wikipedia.org/wiki/Gismonda