Sound is nothing but a form of energy. It travels in the form of waves. When these waves strike the wall the molecules or the atoms vibrate due to the sound energy.
The vibration passes from one atom onto its adjacent atom thus travelling vibration travels through the whole wall and when the wall ends the vibration in turn takes place in the air molecules.
Thus the sound travels through the wall and further into the air. Due to these sound created on one side of the wall can be heard on the other side. This phenomena proves that sound needs medium to travel. In vacuum the sound cannot travel because there are no atoms or molecules present to vibrate. In solids the atoms are packed together tightly than those of liquids and gases.
The vibrations need much less gap between the atoms in order to travel faster. Sound travels more intensely in solids. That is why audible sound passes through hard materials and be audible on the other side.