A prediction market is a place to buy and sell the answer to a question about the future. Somebody asks whether a thing will happen, and instead of arguing about it, people trade on it. The price they trade at is the market's answer, expressed as a probability.
Take a market asking whether a particular team wins their league. It has two sides, YES and NO, and you can buy shares in either. Each share is a claim on exactly $1.00, paid only if that side turns out to be right. A YES share pays $1.00 if the team wins and nothing if they do not. A NO share does the opposite.
Because the payout is fixed, the price does all the work. If YES shares trade at 20¢, the market is saying roughly a 20% chance. Buy one for 20¢ and you are risking 20¢ to make 80¢. If you think the real chance is 35%, that is a good bet. If you think it is 10%, it is a bad one. That is the entire mechanic.
Nobody sets the price. It settles where buyers and sellers stop disagreeing. If a share is cheaper than the true odds, somebody buys until it is not. If it is too expensive, somebody sells. What is left is a number reflecting what the people trading believe, weighted by how much money they are willing to put behind it. It is not always right, but it is expensive to leave obviously wrong.
The early exit is the difference that changes how people behave. A position has a live value every second it is open, so you can take a profit before the event happens, cut a loss when your reasoning breaks, or trade the move rather than the outcome. It also means you can watch a correct call lose money on the way to being right, and then have to decide whether to sit through it.