All publicly sold stock in the US must be listed in one of the US stock exchanges. The most famous is the NYSE (New York Stock Exchange).
This is an ELI5 and vastly simplifies how the market works. The Stock Exchange is basically a market for buyers and sellers to trade shares. Buyers list the shares of what they want to sell (say Apple), quantity (say 500 shares) and price they are willing to sell at ( say $900). Sellers do the same but opposite, what they want to buy, how many and what price they are willing to pay.
When the buyers price and sellers price coincides or overlaps, then a transaction is completed at that price. This sets the “last traded price” that is listed on TV screens or stock market listings. There are many buyers and many sellers and many many transactions happening all at the same time for all the different companies listed on the market. This is what sets the price and why it moves up or down.
If there are buyers willing to pay more for shares, the prices rise. If there are more sellers desperate to sell their shares, the price falls.
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