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First a bit about atom dimensions. If an atom would be the size of a football field, then the nucleus will fit into a space no bigger than one tenth of an inch. All the football field is occupied with electrons. Therefore most space is occupied with negative charge. In solids this negative charge creates bondings between atoms (by beginning to belong to all atoms at the same time- covalent bondings, or by passing to only a single atom and leaving the neighbouring atom depleted of it - ionic bonds). These bonds act like a having a network of forces that hold together all the nuclei of the solid at very short distances. When you try to pass through a wall two things happen. First the two force networks (formed by electron bondings in your body and in the wall) will repel each other because both are negatively charged and occupy almost all of the available space. Second, because they are held together, the nuclei from the wall will not separate one from the other to let the nuclei from your body passing between them. This is why you are not able to walk through a wall.
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