KataGo has multiple components, the two main ones being MCTS, and the policy network. The policy network looks at the board, and gives probabilities for which moves are likely to win. (If that network had “solved” the game, all winning moves would have equal probability, and all others would be 0%.)

But the game is not solved, which is where MCTS comes in. It picks a move, and plays through it, selecting moves that are good but varied, until it learns more about which side would likely win (typically by expanding a leaf of the search tree). Each playthough is a visit. Each visit allows updating its estimate of the win probability for that move, and thus, changes the policy probabilities.

More visits typically anchor the policy estimates into reality further, yielding better play. In fact, this is how the policy network learns.