Intuitive meaning of complex time domain signal representation (quadrature sampling)
One common use of the IQ data from an SDR is to feed them to an FFT.  The upper and lower halves of an FFT result indicated different relationship between the (real) cosine and (imaginary) sine components of the complex FFT result. The direction of rotation of each complex component tells the rest of the signal chain whether the complex component is an upper or lower sideband of the assumed center tuned frequency of the IQ SDR data stream.

The quadrature component in the IQ input is what allows the two halves of an FFT result to not just be redundant complex conjugates of each other (which they would be given a strictly real input, no Q or zero Q).  Thus allowing separating the upper and lower sidebands as independent spectrum.

Also see: https://electronics.stackexchange.com/questions/39796/can-somebody-explain-what-iq-quadrature-means-in-terms-of-sdr/99617#99617