During the early 20th Century, Klimt was a member of Vienna Secession, which was a radical Avant Garde artistic establishment that was based in Austria. Other artists of the time included Auchentaller and Fabiani.
The symbol that was used to represent the group was that of Pallas Athena, who was the Greek goddess of wisdom.
Klimt's art was incredibly decorative and very different from the art that was being produced in Europe at that time. His paintings very much resembled the art that was being painted in France, within the Art Nouveau movement.
The Sunflower represents the very heart of this movement. What we see is an incredibly tall sunflower with a thick, luscious, green stalk with many leaves.