A blood pressure cuff allows paramedics to measure and record your blood pressure. The scientific name of a blood pressure cuff is a sphygmomanometer.
Blood pressure is the pressure of the blood in the arteries. It is constantly changing and can be affected by the rate of the heart beat, the volume of fluid (espicially blood) in the body or a medical problem such as hardened arteries.
Paramedics can measure blood pressure for either medical complaints, such as heart attacks, strokes, etc but also in trauma injuries to establish how much blood a patient has lost.