Why SSB has no carrier, so the receiver must supply one. A product detector is essentially a mixer: it multiplies the incoming SSB signal by a locally generated carrier (the BFO) at the suppressed carrier frequency, and the difference product falls in the audio range. This same circuit demodulates CW as well, which is why SSB/CW receivers share a product detector and BFO.
Watch out A discriminator is an FM detector, converting frequency deviation into audio; phase detectors and phase comparators are PLL building blocks that output a voltage proportional to phase difference, not recovered SSB audio.
Product detector = product (multiplication) of signal and BFO. Discriminator is for FM, product is for SSB/CW.