We and all materials around us are mostly empty space, in the subatomic level. Electrons move about the nucleus in an atom defining the volume of space that the atom occupies. But the nuclei as well as electrons are very small. If an atom were the size of a stadium, one of its electrons would be smaller than a grain of rice and the nucleus would be a single grain of pea at its centre! Furthermore, all the electrons of an atom are widely spaced apart. Atoms are indeed mostly empty space. But when they team up to build chains, through the formation of chemical bonds, networks and ultimately mega-structures or tiny creatures or human beings are produced. A large number of interconnections between their nuclei are established in the process. This is like weaving a large holed net out of very thin thread.
When the atoms of your body push against the atoms of the wall, the electrical repulsions between electrons in your body and electrons in the wall prevent you from passing through the wall. This is like trying to pass one large holed net through another similar net when both of them are fully spread. You cannot pass them until you tear both of them to shreds, in which case, both are destroyed.