It's understood that a runner must advance from first to home by touching the bases in order. Where the confusion comes in for some people is
when the player must go back to their original base. In this case the player must retouch all bases in reverse order. This situation occurs most often
in the following example:
Runner on first base. Ball is hit into the outfield and the runner thinks it's going to drop. He runs past second base and the ball is then caught by the outfielder. He needs to get back to first base before the throw in order to not be forced out.
The correct way for him to do this is to first retouch second base before running back to first. If he runs back to first without retouching second base, the correct call would be for him to be out.
The only exception to the rule is on a dead ball. If the ball goes foul for example, the ball is dead and the player doesn't have to retouch second on his way back to first.