What does the Phase part of a FFT of a received signal represent?
The phases of an FFT result are a phase measurement relative to the time that the FFT input sample window was taken.  Each phase measurement is fairly useless unless you know the absolute time that the sample window was taken, or know the offset of the window from another measurement window (another FFT window with a known overlap/offset/delay/etc., or another window sampled at the same time but offset in space/etc., or some combination of the two), or are comparing or using phases across FFT bins (for reconstruction, convolution, etc.)

Whether the phase is positive or negative depends on how the cosine (or evenness or real) and sine (oddness or "imaginary") components of each DFT result bin relate to each other within the FFT aperture or sample window.  Usually a negative phase indicates the opposite oddness component (hi/low versus low/hi asymmetry) than a positive phase.

If you do an FFT-shift before the FFT, then the phase measurement (the evenness/oddness ratio represented by the atan2 function) is relative to the middle of the vector of samples of the window fed to the FFT, independant of whether the signal is exactly integer periodic in aperture or not.