There is no spoon because nothing in the Matrix is real.
This is a common and ancient philosophy, present in most cultures (in the West we have Plato’s Cave) – nothing in our minds is real. Because we experience the world exclusively through our minds, we seem to experience, a distinct separate world of our minds and the physical world of our bodies. We experience the physical world exclusively through the lens of our minds, so the world seems to be flexible because our minds are flexible.
From a perspective of a Buddhist, “there’s no spoon” is the equivalent to the idea of “There is no self” in Buddhism. The first this was mentioned was in the Oracle’s living room. The robes that those children were in allude to the religion. The idea of no self is that everything is of impermanence and always in a state of flux, even our own “self”; and that It’s wiser not to hold on to any existence as it is. Then a spoon appears to be bent by one of the children in the room.
Another key time that this was mentioned was when Neo was leaving Zion to his final battle. Neo was uncertain and anxious about what to come. One of the children sent Neo a spoon to remind him of the truth that there is no spoon. This is exactly what and how Buddhists practice Buddhism. When one is anxious (sad, angry or even happy), we remind ourselves that there is no self, not even ours. This momental feeling is not and does not own us. This helps us back on track with our “mindfulness” in order to be with the Now and not consumed by the illusion of the past that has already gone and the future which may never come. Now is the only thing that is real and true.
The spoon if thought as a metaphor for obstacles (in our lives), the meaning is profound.
Initially Neo believes that the spoon exists in real and its not possible to bend it. When he is told that the spoon is just a computer code and a part of matrix, reality dawns upon him. He is then able to bend the spoon.
In the same way we have to realize that obstacles (troubles and dufficulties) are just a figment of our imagination. Once we realize this thing then there are no obstacles..
We are the masters of our brains and no obstacle is big enough to stop us from achieving our dreams and goals provided we have the right attitude!