CW - Continuous Wave (Morse Code)
CW is amateur radio's oldest mode. It is a signal of constant frequency and amplitude, switched on and off with a key or electronic keyer to form dots and dashes. At the receiving end, the signal is mixed with a BFO (beat frequency oscillator) to generate an audible signal.
AM - Amplitude Modulation
AM is a modulation technique which uses an audio signal to modulate the strength of a carrier wave. AM signals consist of a carrier signal and two identical sidebands (one above and one below the carrier). AM is very simple to modulate and demodulate, but it is fairly inefficient and susceptible to interference. An AM signal's bandwidth is twice the bandwidth of an equivalent SSB signal, due to the additional sideband.
SSB - Single Sideband
SSB is a more efficient derivative of AM. SSB is essentially an AM signal with the carrier and one sideband stripped away. This results in a signal with half the bandwidth of an equivalent AM signal. SSB increases efficiency at the cost of more complicated radio designs.
SSB is the most common method of voice (phone) communication on the HF bands. Generally the upper side band (USB) is used for 30 meters and up, and the lower side band (LSB) is used for 40 meters and below. There are a few exceptions to this rule, such as 60 meters.