The purpose of a balanced modulator in an SSB transmitter is to:

In a Single Sideband (SSB) transmitter, the balanced modulator is a specialized mixing circuit that combines the original RF carrier with the audio signal from your microphone. Its specific job is to cancel out, or suppress, the RF carrier while passing both the upper and lower sidebands. The resulting output is known as a Double Sideband Suppressed Carrier (DSB-SC) signal. Because the carrier contains no actual voice intelligence and consumes a majority of the power, removing it makes the transmitter vastly more efficient. It is important to remember that the balanced modulator itself does not create a single sideband signal. It passes two sidebands. A subsequent stage, usually a highly selective crystal or mechanical filter, is required to strip away one of the sidebands to finally produce the true SSB signal.