Phase diagram of a rectangular pulse with Fourier Series - help understanding
The phase of a complex number is the angle that the number makes with the positive real axis on a complex(Imaginary vs real) plot. 

Since the coefficients are given by $$a=A \frac{\sin(n\pi/2)}{n\pi/2}$$ it can be seen that it is a real number for any value of n. So $a$ will have a phase of either 0 (for positive number) or $\pi$ (for negative number). Hence whenever the value of $a$ becomes negative the phase is $\pi$.