what is wideband phase shifter in modulator?
See Wikipedia for the mathematical formulation of Single Sideband: it is a special case of quadrature modulation, in which the quadrature signal is derived directly from the in-phase signal by a 90-degree phase shift. The Wideband Phase Shifter in your diagram produces the Q signal from the I signal (taken as the input).

Your diagram was traditionally known as the Phasing Method of SSB generation (in contrast to the Filter Method). It is difficult to accomplish an accurate 90-degree phase shift over a wide band (even a typical audio bandwidth) with passive components, which is why the Filter Method has dominated SSB generation until recently. Modern DSPs implement a Hilbert transform to accomplish the phase shift, dramatically reducing the cost, size, weight and power consumption of an SSB generator.