Electrical Force:

What makes a solid act as it does? Why, when you place a concrete block on a concrete floor, does the block not slowly sink into the floor or meld with the floor and hence you cannot pick it up again later? Why, when you strike a brick wall with your fist, are you likely to hurt yourself instead of having your fist go into the bricks? Internally, atoms are typically empty space; this is true even in the most dense solids we see on Earth. Why can't solid objects pass via one another the way galaxies sometimes do in outer space or the way dust clouds do in the atmosphere? They are mostly empty space too, and they can pass through each other simply.

The answer to this question lies in the nature of the electrical forces in and around atoms. Every atomic nucleus is bounded by "shells" of electrons, all of which are negatively charged. The objects with electrical charges of the same polarity (i.e., positive-positive or negative-negative) always repel each other. The closer altogether two objects with like charge come to each other, the more forcefully they repel. Therefore, even whenever an atom has an equivalent number of electrons and protons and hence it is electrically neutral as an entire, the charges are concentrated in diverse places. The positive charge is contained in the nucleus, and the negative charge surroundings the nucleus in one or more concentric spheres.

Assume that you could shrink down to sub-microscopic size and stand on the surface of a sheet of, state, elemental aluminum. What would you see? Below you, the surface would emerge something like a vast field full of basketballs as shown in figure below. You would find it hard to walk on this surface since it would be irregular. Though, you would find the balls fairly resistant to penetration by other balls. All balls would be negatively charged; therefore they would all repel each other. This would remain them from passing through each other and also would keep the surface in a fixed, stable state. The balls would be generally empty space inside, though there wouldn't be much space in among them. They would be just about as tightly packed as spheres can be.

Figure: In a solid, the outer electron shells of the atoms are tightly packed. (This drawing is very much oversimplified.)

The foregoing is a generalization, though it must give you an idea of the reason why solids generally don't pass through each other and however why many solids resist penetration even by liquids like water or gases like air.