A delay between player input and corresponding visual feedback creates a strange, unnatural feeling and makes it hard to move or aim precisely. Client-side input prediction (cl_predict 1) is a way to remove this delay and let the player's actions feel more instant. Instead of waiting for the server to update your own position, the local client just predicts the results of its own user commands. Therefore, the client runs exactly the same code and rules the server will use to process the user commands. After the prediction is finished, the local player will move instantly to the new location while the server still sees him at the old place.
After 150 milliseconds, the client will receive the server snapshot that contains the changes based on the user command he predicted earlier. Then the client compares the server position with his predicted position. If they are different, a prediction error has occurred. This indicates that the client didn't have the correct information about other entities and the environment when it processed the user command. Then the client has to correct its own position, since the server has final authority over client-side prediction.
