Or any other cryptocurrency for that matter. Does the Cardano blockchain have inherent knowledge of the current value of ADA, or is it oblivious to price? Who/what determines how many USD (or another fiat currency) is 1 ADA worth at a given point in time?
The market decides. Supply and demand. If there is someone willing to pay more for the currency, the price will go up, and if no one will buy at the current price, sellers are forced to lower the price.
Different exchanges might have different prices, but they will naturally even out as people arbitrage the difference away.
The network is "oblivious" to all of this. There is nothing in the inherent protocol of Cardano that maps the value of ADA to any fiat currency. Information from off-chain can only be consumed on-chain with the help of Oracles and other such services.