Before everyone starts explosively typing essays about why a stock's price is virtually impossible to predict, I want to iterate that I am not asking how to know what a stock's price will be. I am asking what mechanism is actually responsible for changing the stock's price. Not the multitude of factors that influence it, but literally what is changing the number. Why is a stock's price $43.56 one second, and then $43.57 the next? What changed the number? A computer program? If the answer is something like 'an algorithm changes the number based on what people are willing to pay for it', what does that even mean? What number would anybody be paying for the stock other than its instantaneous price? Does more and more people purchasing at $43.56 tell the algorithm 'lets move it to $43.57 and see if people continue to buy at the same/increased rate'?
The stock market is an auction with buyers and sellers looking to acquire different amounts of stock at any given moment in time.
If there is a net excess of buying volume, price rises. If there is a net excess of selling volume, price declines. When buying and selling is in equilibrium, price does not change.
It's simply a tug of war between supply and demand.