What does actually the "unravel branch wrap" option do to the phase plot in LTspice?
It adds or subtracts multiples of \$2\pi\$ (360 degrees) to each point in the phase plot so that the phase is plotted continuously rather than having jumps in it. 

We know that physically the phase is going to be continuous from frequency to frequency. However as the output of the analysis is a vector gain at each frequency, all angles are reduced to the base range of +/- 180 degrees, so the graph has no way of knowing at any one frequency how many times phase has wrapped around the circle.