The meaning of the gesture is very starightforward: called "фига" (figah) in Russian, it is a direct analog of a stretched middle finger.

These days, a middle finger is also known among Russians but it is relatively new Western influence, while a figah has been widely used for centuries...

RE: II

II-gave absolutely incorrect explaination of FIGA meaning.
No analogy with the middle finger watsoever. Middle finger in English is an insulting gesture meaning "F* you!" It is shown when the speaker is mad at, or at least very unhappy with some other person's behavior. It demands an agressive response, most likely the same gesture or a fight.
FIGA ( synonims SHISH, KUKISH) has different usage. No f*** business at all. You can not show FIGA to somebody who cut you off on the road. It would be laughable. FIGA will not work if you want to insult the opponent or to provoke a fight.
It is a pretty innocent gesture, and not insulting for those who know Russian life better than "II".
FIGA is shown only in response for someone's reguest or demand of something, and means a strong denial. The best way to show the FIGA is to move it as close to the demander's nose as possible.
It means "you will never get what you ask me for". It may be replaced with it's verbal equivalent: "Фигу тебе!" or "Фигу вам!" It used to be an impolite gesture if used by adults but nowdays is used mostly by kids, some low educated women or in zest. One can find it in many cartoons and books for children ("Cheburashka and Gena the Crocodile", "The Tree from Prostokvashino").
The adult men use some stronger words the Russian language is rich with.
The middle finger is a Western stuff. It is in fashion in Russia now, but I consider it unpatriotic. And petty. What is a finger after all? Too small.
We Russian always showed a forearm bent in elbow joint with the fist instead of the middle finger. A real man gesture! I can teach:
Use either of your arms. Make the fist. Bent the arm in the elbow making a straight angle with the shoulder which is along the side of your chest. Now (very important) put the palm of your other hand on the biceps muscle of the first arm (the one with the fist), like you are measuring off some part of it to show the size. And now, keeping the original angle approximately straight, push the whole composition a little bit forward to show it to your opponent.
This is the middle finger in Russian.
But we are not the mega-size rudest people in the world. I heard, they show the whole arm with the fist (measured from the shoulder) in Turkey.

OK, we got enough of fun, let's go back to the business.

Though it is not always easy understand what was in the ENUMERATOR's surrealistic head I think I can try...

I think the meaning of the catrtoon is the following:
"You want (expect) real, good Presidential elections in 2008? With all these candidates running and you choosing from them?
ФИГУ ВАМ! (FIGA to you!) You will get the ПРЕЕМНИК (SUCCESSOR)!( this word is written on the thumb, the only finger sticking out forward and facing the face of the person to whoom the FIGA is shown). All the other candidates (names on the other fingers) are used as just a decorative wrapping for the thumb (the SUCCESSOR).

In other words: "People! Do not try to guess who will be the next President. Do not think you will choose Medvedev, Ivanov or Kasyanov. You will get the SUCCESSOR.

In addition

The hand is Putin's one