What does a Sphygmomanometer measure?

It measures blood pressure. This is the force of blood pushing against the inside of the blood vessel walls. When someone is taking your blood pressure they are actually trying to hear it.

The typical sphygmomanometer consists of an inflatable cuff and a pressure-measuring device called a manometer. The person taking your blood pressure inflates the cuff around your upper arm and places a stethoscope on the inside of your elbow. As they let the pressure out of the cuff they listen for a "swooshing" or thumping sound. They record the reading on the manometer when they first hear the sound and when they last hear the sound. So if they first hear the sound when the manometer reads 120 and they last hear the sound it when it reads 80, your blood pressure is 120 over 80. They would write this as 120/80.

The word "sphygmomanometer" is a combination of the Greek word sphygmus, which means "pulse" and the term manometer. A manometer is a device that measures pressure using a column of fluid. In 1896, Dr. Scipione Riva-Rocci of Italy introduced a mechanical sphygmomanometer similar to what we use today. It was the first simple solution that gave fairly accurate measurements. The manometer in Dr. Riva-Rocci's device used mercury as the fluid.

Today's mercury sphygmomanometers are very accurate and they don't require recalibration. A column of mercury can be difficult to carry around and mercury isn't an environmentally friendly substance.  For these reasons Aneroid sphygmomanometers, like the one pictured above, are very popular.  They use a small mechanical device with a convenient dial to measure pressure.  They do require recalibration.

Digital sphygmomanometers are even more convenient than Aneroid sphygmomanometers, especially in noisy places. Instead of sound they use vibration to determine diastolic and systolic pressures.  Blood flowing though arteries at higher than normal pressure cause the artery walls to vibrate.  Digital sphygmomanometers detect the changes in these vibrations as the pressure in the cuff is released.