A superheterodyne receiver designed for SSB reception must have a beat-frequency oscillator (BFO) because:

Single Sideband (SSB) transmission is highly efficient because it suppresses the carrier wave and one of the sidebands before the signal is transmitted. However, this means the receiving station only receives a single sideband containing the voice information, without the steady reference carrier needed to properly demodulate it. To recover the original audio, the receiver must reinsert a local version of the missing carrier. This is exactly what the beat-frequency oscillator (BFO) does. It generates an unmodulated signal that 'beats' against the incoming sideband in the product detector, allowing the original audio frequencies to be extracted. The BFO does not replace the missing sideband, nor does it filter the pass-band; it strictly replaces the suppressed carrier so that detection can occur.