The concept of Lucid Dreaming fits well within the framework of The Matrix. Many times other characters refer to The Matrix as a dream from which you cannot wake:
Morpheus: Have you ever had a dream, Neo, that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world?
However a lucid dream is a dream in which one is aware that one is dreaming:
In a lucid dream, the dreamer may be able to exert some degree of control over their participation within the dream or be able to manipulate their imaginary experiences in the dream environment.
Thus the truth that 'Spoon Boy' is reinforcing for Neo is that he is in a dream and that he only needs to truly comprehend this in order to become lucid.
Spoon boy: Then you'll see, that it is not the spoon that bends, it is only yourself.
Thus when Neo repeats this mantra to himself he is reminding himself that it it is only his awareness of being in a dream that matters.
This also functions as part of the plot which falls readily into the pattern of the hero's journey:
the hero begins in the ordinary world, and receives a call to enter an unknown world of strange powers and events. The hero who accepts the call to enter this strange world must face tasks and trials, either alone or with assistance. In the most intense versions of the narrative, the hero must survive a severe challenge, often with help. If the hero survives, he may achieve a great gift or "boon."
The concept of being within a dream, awakening from it, and finally gaining control over it is shown throughout the film.