The top of the female part of the flower which receives pollen, which forms a tube that grows down the style to deliver pollen to the ovary, which develops into fruit/seed.
Image Above: The parts of a flower, including the stigma.
For additional information: http://en.wikipedia.org/wiki/Stigma_(botany)
Image from URL: http://www.uic.edu/classes/bios/bios100/summer2004/lect15.htm