What does influence Bitcoin price so much? Please, make a hint why bitcoin price fluctuates so much almost every day. Is this fluctuation artificial? How is it organised?

As far as I know, there are already 12 million of bitcoins. On stock exchanges traders sell or buy rather modest sums, about hundreds or thousands of coins. 

How can this influence (price drop of 10% a day) millions of other bitcoins so much?
The market is full offer and demand based. People sell, price goes down. People buy, price goes up.

The amount of people with new capital entering the market push the price up hard. Harder than the new Bitcoins, obtained through mining, are pushing it down.

You have to realize that people have to choose to sell or buy Bitcoin. The amount available is called "market depth" and it causes "market liquidity". http://mtgoxlive.com/ Is a display of "market depth". You can mouse over the blue and orange lines to see how many bitcoins must be bought or sold to bring the price to a certain point.

Then you will see that the 4684 bitcoins must be sold (at prices offered by others) to bring the best-available price to 550 Euros. To bring the price up, 3687 bitcoins must be bought to bring the best available price to 750 Euros.

Exchanges, real-time bids on Bitcoin for Euro or Euro for Bitcoin, are a method to find the "right price" of Bitcoin. Real-time exchanges fluctuate in the real world a lot too. It doesn't really work that well. But it succeeds in creating an acceptable price (if someone wishes to buy it for that price, it's worth that), and that's why the other Bitcoin are affected. People accept the spot price set by the people that use the exchanges.