Physical meaning of reflection coefficient being complex
it just means that the reflection coefficient can be represented as a complex number/quantity in the form : 

a +jb or in polar notation using magnitude and angle.

It doesn't have any "physical" significance or so. Its just a mathematical tool to represent the nature of a quantity and simplify calculations. For eg: when we represent an impedance as a complex quantity, Z = a+jw , we can infer that a there is a real part which doesn't vary with input voltage (Resistance), and there is an imaginary part jw ( Reactance part due to inductors and capacitors), which can varies with input voltage frequency.