The SI unit of pressure is the **Pascal (Pa)**, where 1 Pa = 1 N/m2, i.e. one Newton per square meter. The Newton is the unit of force, so it's easy to see that the Pascal meets the requirements for a unit of pressure. However, the Pascal is quite a small unit for things like atmospheric pressure, so there are quite a large number of alternatives also in use. One of the simplest ways to do this is to simply use kPa (i.e. kilopascals, or thousands of pascals), but there are other options too.
The most well-known alternative unit is **pounds per square inch (psi)**, which is used in the U.S. for things like water pressure. For atmospheric pressure, the appropriately-named unit "atmospheres" (atm) is often used, because 1 atm corresponds to atmospheric pressure at sea level. The torr is an alternative unit used for atmospheric pressures, which is defined as 1/760 of an atmosphere, or 133.3 Pa. In meteorology, millibars are often used, where 1 bar = 100,000 Pa and 1 millibar = 100 Pa.
Finally, there are some even more unusual units for pressure, including millimeters of mercury (mmHg), which is defined based on the pressure exerted by a 1 mm tall column of mercury and is often used for blood pressure.
This was originally the intention of the torr, and so it shouldn't come as much of a surprise that the two are essentially the same: 1 mmHg = 133.322 Pa. Finally, in some cases pressure is measured as a value in dyne per square centimeter. Here, the dyne is a unit of force with 1 dyne = 0.00001 Newtons, and so 1 dyne per square centimeter equals 0.1 Pa.