The price is just the most recent price it sold at. Imagine a town with identical houses. You own a house there. If the last house sold for $500,000 you can say yours is also worth $500,000 because they are identical. But when you go to sell yours you have to negotiate the price with a buyer. You sell yours for $520,000 so now all the other houses can claim that value.
Stock trades are closely monitored by stock exchanges so it is easy to see the most recent trades.
If you use robinhood or something similar you are trading on margins. You don’t actually own the stock but the company you trade though promises to respect the value of the stock based on the most recent trades on the stock exchange.
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