Why has a gas two values of molar heat capacities?

Gasses have two specific heat capacities because the boundary conditions can affect the number by up to 60%. Therefore, a number is given to each boundary condition: isobaric (constant pressure) or isochoric (constant volume). In an ideal gas, they differ by the quantity R (the gas constant - the same one you use in the ideal gas law):

Cp = Cv + R

where Cp is the isobaric molar heat capacity (specific heat) and Cv is the isochoric molar heat capacity.