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'Reduced-carrier transmission' is an amplitude modulation (AM) transmission in which the carrier wave level is reduced to reduce wasted electrical power. 'Suppressed-carrier transmission' is a special case in which the carrier level is reduced below that required for demodulation by a normal receiver.
Reduction of the carrier level permits higher power levels in the sidebands than would be possible with conventional AM transmission. Carrier power must be restored by the receiving station to permit demodulation, usually with a beat frequency oscillator (BFO). Failing to match the original frequency when receiving such a signal will cause a heterodyne.
Suppressed carriers are often used for single sideband (SSB) transmissions, such as for amateur radio on shortwave. International broadcasters agreed in 1985 to also use suppressed-carrier SSB entirely by 2015, though IBOC and IBAC digital radio (namely Digital Radio Mondiale) seems likely to make this irrelevant
A double-sideband suppressed carrier (DSSC) from a stereo generator is used as a subcarrier to transmit FM stereo.
Source: partly from Federal Standard 1037C
See also Carrier recovery.