Do both H (enthalpy) and ∆H, or ∆H alone have a physical significance? My chemistry teacher said that H (enthalpy) alone has no physical significance it is ∆H or change in enthalpy that has a physical significance. But my book says that both have a significance and H alone represents the total heat content of the body. Thus I am in a confusion, please help me.
Offcourse H and ∆H have physical significance. H represents the enthalpy of a system. Enthalpy refers to the sum of the internal energy of a system plus the product of the system's pressure and volume. 

The ∆ symbol is used to represent change. Therefore, ∆H represents the change in enthalpy of a system in the reaction. So your book is completely correct.