What does imaginary Component of a bin's phase in the Fourier Transform mean?
It simple trigonometry.  A vector (FFT result bin) can have a magnitude and a phase.  Or you can specify the same vector identically with X,Y coordinates.  The complex representation simply uses X for the real part and Y for the imaginary component.  Without an imaginary component, there’s no place to put the Y, and your vector would be under specified.

The phase ends up being atan2(I,Q) == atan2(Y,X) == atan2(im(z),re(z))

As for why use a complex representation rather than 2 strictly real quantities?  The complex math is more elegant, and requires less writing on the chalkboard to demonstrate similar things.