What's the meaning of the Buddhist boy's message to Neo in the movie The Matrix?

The Matrix film franchise is, prima facie, confusing emptiness as mu only, meaning there is no reality and everything is illusion only. In fact, every western philosophical interpretation or work of scholarship I've read claims that the conventional truth can be used to predict the future.

This is the "middle way"

Or, more generously, it is a demonstration that meditation on emptiness can develop supernormal powers.

"There is no spoon" can mean a bunch of things in the Buddhadharma. It could be that "there is no spoon" because the spoon is actually a composite of mereological reals and has no independent existence as a "spoon" apart from its components. Once, while she was meditating deeply in the dark woods, Vajrābhikṣuṇī ("Vajirābhikkhunī" in Pali) heard the voice of Mara. Mara asked her:

Who created this being? Where is its maker? Where has the being arisen, and where does it cease?”

Sister Vajrā addressed the haughty godling:

Why now do you[, Mara,] assume ‘a being’? Mara, is that your speculative view? This is a heap of sheer formations [i.e. "saṅkhārā"]: here no being is found. Just as, with an assemblage of parts, the word ‘chariot’ is used, so, when the aggregates exist, there is the convention ‘a being.’ It’s only suffering that comes to be, suffering that stands and falls away. Nothing but suffering comes to be, nothing but suffering ceases.

(SN 5.10 Vajirāsutta)

There is no "being" in the same way as "there is no spoon" and there is "no chariot."

What's the meaning of the Buddhist boy's message to Neo in the movie The Matrix?

It means that when one truly understands (through insight meditation) the Three Marks of Existence, then one can become free from suffering - no more ignorance and craving. One has become Enlightened, one has reached Nibbana.

In this scene from the first movie in The Matric trilogy, when Neo goes to meet the Oracle he meets the Buddhist boy who shows him that he can bend the spoon and then tells him that he can do the same when he can realize that 'there is no spoon', that when you see the spoon bending, it is really yourself that's bending.

That there is no spoon means that there is no permanence, no satisfaction and no control over conditioned existence.

That it is really oneself that is bending means that when ignorance has been dispelled one will finally see only ultimate reality.

Please read this answer to understand papañca (objectification-classification, reification, concept proliferation) in Buddhism.

Please also read the following story from this Quora answer to understand that "there are no ghosts of a woman and child crying at night", it's really just "you".

In the middle of the night I woke up from my sleep and could not go back to sleep as I was feeling terribly home sick.

At home I was used to a small night light in my room. But there (girls' hostel), there was no night light. It was pitch dark.

I was just tossing in my bed and then I heard this bone chilling high pitched cry.

It was like a woman crying in pain. After few minutes (or seconds) another cry was mixed with the first. It was like a baby cry.

These two sounds continued for, what seemed like very long time. But it might be for one or two minutes or may be less than a minute.

I was damn scared. I didn’t know what to do. Everything was new for me.

I wanted to go to some other girl’s bed and sleep beside her. But I was afraid that I may be scolded.

I was surprised how other girls were sleeping (soundly) when there is such high pitched horrifying noise. ...

The whole night I could not sleep thinking about that sound. In the morning I sat on my bed and started to weep.

One girl, three or four years senior to me, came to me and asked why I was crying.

I told her what happened at mid night and how scared I felt.

She laughed and cajoled me.

“Do you know what that sound is?” she asked.

“May be ghosts?”

“No, they are cats!”

“Cats? Are you sure?”

“Yes one male cat and one female cat. We are hearing those sounds from two years. We are used to those sounds. So we are not afraid any more. When I heard it first time, even I could not sleep that night”

“But they were very loud”

“Because one side of our building is empty in the night, and because the cats are in underground floor, the sound reverberates and makes it more horrific”. ...

Later I learned that cats make this weird sound when they are mating. The male cat’s cry will be more horrifying.

It makes sense within the context of the movie -- being that "the Matrix" is a "simulation".

I've read Thich Nhat Hanh describe "inter-being" as follows:

Suppose I hold a leaf in my hand. What do you see? A leaf is a leaf; it is not a flower. But in fact, when we look deeply in to the leaf, we can see many things. We can see the plant, we can see the sunshine, we can see the clouds, we can see the earth. When we utter the word “leaf”, we have to be aware that a leaf is made of non-leaf elements. If we remove the non-leaf elements, such as the sunshine, the clouds, and the soil, there will be no leaf left. So it is with our bodies and ourselves. We’re not the same as, nor are we separate from, other beings. We’re connected to everything, and everything is alive.

I think that's one of the aspects of emptiness ("If we remove the non-leaf elements there will be no leaf left").

I think that Zen is a bit ambivalent on the subject:

At the first level on the path he saw mountains as mountains and rivers as rivers.

On the second level of the path he saw that mountains are not mountains and rivers are not rivers.

And at a third level he saw once again mountains were mountains and rivers were rivers.

I think of it as a partial truth; possibly extremist (i.e. one side not the other, not the middle way); possibly dangerous, useful to justify immorality (e.g. "it doesn't matter if you kill people because they don't exist anyway"); possibly conceptual proliferation, letting intellectual theories run away without regard to fact. But partially true.

I think some of the facts of the matter are ably explained by the Zen story, Nothing Exists:

Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.

Desiring to show his attainment, he said: “The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no realization, no delusion, no sage, no mediocrity. There is no giving and nothing to be received.”

Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.

“If nothing exists,” inquired Dokuon, “where did this anger come from?”

The meaning of the phrase -- the way in which it may be meaningful or useful outside the movie -- might be illustrated by Persig's old South Indian Monkey Trap ...

... the most striking example of value rigidity I can think of is the old South Indian Monkey Trap, which depends on value rigidity for its effectiveness. The trap consists of a hollowed-out coconut chained to a stake. The coconut has some rice inside which can be grabbed through a small hole. The hole is big enough so that the monkey's hand can go in, but too small for his fist with rice in it to come out. The monkey reaches in and is suddenly trapped...by nothing more than his own value rigidity. He can't revalue the rice. He cannot see that freedom without rice is more valuable than capture with it. The villagers are coming to get him and take him away. They're coming closer -- closer! -- now! What general advice...not specific advice...but what general advice would you give the poor monkey in circumstances like this?

... i.e. "there is no trap".

One other thing from the movie, as Neo gains in ability they say of him, "He's starting to believe." Focus on non-existence (e.g. of impediments) can be helpful I guess, another aspect of Buddhism that perhaps isn't so famous in popular culture is a focus on developing factors of enlightenment.