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.
This is a single sideband modulator.
The message signal m(t) is assumed complex. It may be the output of a baseband QPSK modulator for instance. The wideband phase shifter takes each frequency component in that signal and supplies it 90 degrees out of phase to the two product modulators (aka multipliers). Together with the 90 degree phase shift of the carrier signal fc, this means that when the two products are recombined in the adder, m(t) will have been single sideband modulated onto fc.
In slightly more mathy terms, for each frequency fm in the message, the output will contain a frequency of fc+fm, or fc-fm (depending on the polarity of the modulators), but not both.
Bear in mind that as m(t) is complex, it has both positive and negative frequencies, thus the need to continue to keep them apart when modulated up on the carrier.
If terms like QPSK, baseband, the concept of negative frequency or a complex signal are puzzling to you, you will need to do a lot of background reading. This answer space is too small for a complete signal processing and communications course.