Voltage Controlled Amplifier (VCA)   

A voltage controlled amplifier accepts a voltage at its input and outputs an increased voltage proportional to its gain setting.  If an amplifier accepts a control signal which alters its amplification characteristics it is a voltage controlled amplifier (VCA). 
An amplifier in an analogue synthesizer which changes its amplification according to the size of a control voltage. 

For example 
0 volts = no signal, 
10 volts = maximum amplification of the signal. 

A transient envelope is often the source of the control voltage.

A varying signal can be used as a control signal for a VCA to acheive amplitude modulation. 

A special case of amplitude modulation is achieved by use of a device which generates a complex function which starts at zero and passes through a sequence of levels at some rate and ends in zero again. When this control signal is applied to a VCA the resulting combination is useful in envelope shaping applications.