Skin in the game changes behavior
A pundit predicting an election outcome on television faces no direct cost for being wrong. Their incentive is often to be interesting, confident, or aligned with an audience, not necessarily accurate. A trader in a prediction market faces the opposite incentive: if they bet according to what they merely wish were true rather than their genuine best estimate, they tend to lose money to traders who bet more carefully. Over many participants and many trades, that financial pressure pushes prices toward honest, well-considered estimates rather than confident-sounding guesses.
This is sometimes called the wisdom of crowds, but it's more specific than a simple average of opinions. It's an average weighted by conviction and willingness to risk money, so people with strong, well-founded information have more influence on the price than people who are just guessing.