Sample and Hold is a circuit that is used to take a changing analog signal and literally hold it so that a following circuit or system such as an ADC, (Analog to Digital Converter) has the necessary time it needs to process it. At its simplest, a sample and hold circuit is a capacitor and a switch. The capacitor is used to store the analog voltage for a short time and an electronic switch is used to alternately connect and disconnect the analog input to the capacitor. When the switch closes, the capacitor charges up to, or discharges down to the input voltage. This is the sampling function. Once the switch opens, the voltage across the capacitor remains constant since no current can flow due to the infinite resistance created by the open switch (hold). However, the voltage across the output is still measurable. In the real world, resistance can never be infinite, thus the voltage stored in the capacitor will decay slowly. The quality of a sample and hold circuit is measured by the rate of the voltage decay. The rate at which the switch opens and closes is the sampling rate of the system.
Sample and Hold sections are found on some of the older synthesizers made by Moog and ARP. Taking a random input from a noise generator and turning it into a variety of musically useful effects was the most common use of the S & H section.