Cryptocurrencies are a free market. The price of a cryptocurrency like Chainlink is determined by supply and demand. There is no central authority that can have a direct influence on the Chainlink course.
The price of a LINK increases when the demand for the cryptocurrency is high. Investors promise themselves high profits, they trust the project behind the crypto currency and that it will succeed. Or you want to buy Chainlink to run a node yourself.
At the same time, the Chainlink price falls when investors prefer to sell the cryptocurrency rather than buy it. This can happen because they want to realize profits, because they no longer believe in the project or a generally bad mood prevails in the crypto market.
Chainlink is traded on many platforms. The average price of these platforms then results in the global average price. The market capitalization is calculated from the price of a single LINK token and the total amount available.