In the movie Dorothy's ruby slippers represent a couple of things one being Dorothy and her own potential power. The other being the little guy's ability to triumph over powerful forces.
At the start of the movie Dorothy is a fearful, naive girl who is not confident in her ability to complete her journey back to Kansas by herself but as the movie progresses she unknowingly starts to become more confident in herself and her ability to face challenges independently. The other symbolism of the slippers is shown in the film by Dorothy winning against The Wicked Witch of the West.
Here is the scene where Dorothy receives the slippers.
In the scene the Wicked Witch of the West wants the slippers but Glinda removes them and gives them to Dorothy before the witch can get them causing frustration and anger. At this point Dorothy is unaware of how powerful they are and how they can help her.
Overall the slippers are an important symbol to 'The Wizard of Oz' because of how they display Dorothy's ability to overcome obstacles that she is faced with through the movie.