why specific heat capacity of a substance is greater in liquid state than in solid state?

beacause, the molecules in solid are tightly packed and heat transfer is easy whereas in liquid molecules are relatively far therefore it needs more heat to transfer!!

Heat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that shows the amount of heat required to change the temperature of a substance by a given amount. In the International System of Units (SI), heat capacity is expressed in units of joule(s) (J) per kelvin (K).

Derived quantities that specify heat capacity as an intensive property, i.e., independent of the size of a sample, are the molar heat capacity, which is the heat capacity per mole of a pure substance, and the specific heat capacity, often simply called specific heat, which is the heat capacity per unit mass of a material. Occasionally, in engineering contexts, a volumetric heat capacity is used. Because heat capacities of materials tend to mirror the number of atoms or particles they contain, when intensive heat capacities of various substances are expressed directly or indirectly per particle number, they tend to vary within a much more narrow range.

Temperature reflects the average kinetic energy of particles in matter while heat is the transfer of thermal energy from high to low temperature regions. Thermal energy transmitted by heat is stored as kinetic energy of atoms as they move, and in molecules as they rotate. Additionally, some thermal energy may be stored as the potential energy associated with higher-energy modes of vibration, whenever they occur in interatomic bonds in any substance. Translation, rotation, and a combination of the two types of energy in vibration (kinetic and potential) of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of atomic matter (loosely bound electrons occasionally also participate). On a microscopic scale, each system particle absorbs thermal energy among the few degrees of freedom available to it, and at high enough temperatures, this process contributes to a specific heat capacity that classically approaches a value per mole of particles that is set by the Dulong-Petit law. This limit, which is about 25 joules per kelvin for each mole of atoms, is achieved by many solid substances at room temperature (see table below).

For quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the specific heat capacity will be a fraction of the maximum. As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom. Quantum theory can be used to quantitatively predict specific heat capacities in simple systems.

Water has a high specific heat due to hydrogen bonding which increases intermolecular forces between molecules. See the detailed answer below for more information.

We should first start with a definition: The specific heat is the amount of heat (energy) needed to raise a one gram of a substance by one degree Celsius. Essentially this means that if you have 5 grams of A that has a high specific heat, and 5 grams of B with a low specific heat, you''re going to have to put more heat into substance A in order to get the same temperature change as substance B. Put another more general way: it is difficult to change the temperature of substances with a high specific heat because they resist change in temperature. 
First we have to take a look at what''s going on when a substance increases temperature. Temperature is the average kinetic energy of the molecules, meaning the faster the molecules move, the higher the temperature. The slower the molecules move, the lower the temperature. When you add heat to a substance, it gives the molecules more energy, they will move faster, and the temperature will increase. 
So now let''s look at water. We already know that water has considerable resistance to change in temperature and therefore a high specific heat. We see this characteristic when the pot of water takes forever to boil and when bodies of water act as a buffer during weather shifts. The reason for water''s high specific heat lies with the molecular structure of the H2O molecule. 
The two hydrogen atoms share electrons in a covalent bond with the oxygen. But they are shared unevenly--that is, the bond between the hydrogen and oxygen is a polar covalent bond. The oxygen is more electronegative and is more attracted to the electrons. Because electrons are negative, the oxygen atom becomes slightly negative and the hydrogen atoms become slightly positive. This difference in charges and the bent nature of water contribute to its "dipole moment." The slightly negative oxygen of one water molecule is going to be attracted to the slightly positive hydrogen of another molecule. This attraction is called a hydrogen bond. Because of these bonds between water molecules, they "stick" to each other (or have increased intermolecular forces). 
Let''s put the hydrogen-bonding water molecules and the ideas of temperature together. To get a given sample of water to increase its temperature, you''re going to put heat into it. This heat works to move the molecules faster. But there''s something holding the water molecules from moving freely -- they are "stuck" together to a certain extent because of their hydrogen bonds. The heat you''re putting into the water goes to increasing movement and into the hydrogen bonds. Some of the energy is taken away because the hydrogen bonds first have to be broken. 
Although hydrogen bonds don''t involve sharing or transferring of electrons and are a lot weaker than covalent bonds, a lot more energy is needed to overcome them. Thus, the hydrogen bonds in water make it difficult for it to change temperature; it has a high specific heat.Rate This Answer