Do both H (enthalpy) and ∆H, or ∆H alone have a physical significance?
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.