Every share on Polymarket pays exactly $1.00 if its outcome happens and $0 if it does not. That one rule is what makes a price readable as a probability. A share trading at 30¢ is the market saying there is roughly a 30% chance. Nothing more complicated is going on underneath.
Because the payout is fixed at $1.00, the only thing left to negotiate is how likely the outcome is. If enough people think an event is a coin flip, they will pay up to about 50¢ for a share and no more, because paying more than 50¢ for a coin flip loses money over time. Push the odds up and the price follows. That is why prices are quoted in cents and why they sit between 1¢ and 99¢. A price of exactly $0.00 or $1.00 would mean the question is already settled.
Read it in the other direction too. Buying at 30¢ means you need this outcome to happen more than about 30% of the time to come out ahead. That is the whole bet, stated in one number.
Polymarket does not set prices. Traders do, through an order book. Buyers post the prices they are willing to pay, sellers post the prices they will accept, and when the two meet a trade happens. Nobody is standing behind the market guaranteeing you a quote, which is why a price is only good for as many shares as are actually posted at it.
Prices move for one reason. Someone was willing to trade at a different price than the last person. What makes them willing varies. News arrives, a poll lands, a game turns, someone with a large position needs to get out, or a big buyer clears the cheap shares so the next buyer has to pay more. In an active market all of that happens in seconds, which is exactly why a copied trade can fill a step away from the price the trader you copied got.