When energy is applied to a liquid, its particles can move around faster. Energy applied to a gas will make its particles move around faster and farther, since they are not confined to one volume as they are in a liquid.
Solids however are made from arrays of molecules that are fixed in place. Each molecule contains atoms locked in place by interatomic forces. The atoms can't move around within the solid. How then does a solid store energy, if its particles can't move around within the material?
One way that a solid can store energy is by allowing its particles to vibrate. In other words, although the atoms are locked in place within a molecule, they are free to move back and forth a little. This allows them to store energy. All solids that exist at temperatures above absolute zero are made from molecules whose atoms are vibrating in this way. Here is an animated picture of a special type of solid called a crystal, where the atoms form regular patterns. You can clearly see the movement of atoms within the crystal molecule.