An introduction to pressure - the definition and presentation of common units as psi and Pa and the relationship between them: 

Pressure in a fluid is defined as "the normal force per unit area exerted on a imaginary or real plane surface in a fluid or a gas". 

The equation for pressure can expressed as: 
p = F/A         (1) 
where 
p = pressure [lb/in² (psi)        or lb/ft² (psf)        or N/m²       or kg/m² (Pa)]
F = force [lb⁽¹⁾, N] 
A = area [in² or ft², m²]

⁽¹⁾ In the English Engineering System special care must be taken for the force unit. The basic unit for mass is the pound mass (lb_m) and the unit for the force is the pound (lb) or pound force (lb_f). 

Absolute Pressure
The absolute pressure - p_a - is measured relative to the absolute zero pressure - the pressure that would occur at absolute vacuum. 

Gauge Pressure
A gauge is often used to measure the pressure difference between a system and the surrounding atmosphere. This pressure is often called the gauge pressure and can be expressed as:

p_g = p_a - p_o      (2)
where 
p_g = gauge pressure
p_o = atmospheric pressure

Atmospheric Pressure
The atmospheric pressure is the pressure in the surrounding air. It varies with temperature and altitude above sea level. 

Standard Atmospheric Pressure
The Standard Atmospheric Pressure (atm) is used as reference for gas densities and volumes. The Standard Atmospheric Pressure is defined at sea-level at 273^oK (0^oC) and is 1.01325 bar or 101325 Pa (absolute). The temperature of 293^oK (20^oC) is also used.

In imperial units the Standard Atmospheric Pressure is 14.696 psi.
101.3 kPa = 1 atm = 14.696 psi = 760 mmHg = 760 torr 

Pressure Units
Since 1 Pa is a small pressure unit, the unit hectopascal (hPa) is more widely used, especially in meteorology. The unit kilopascal (kPa) is commonly used in technical applications as HVAC systems, piping or similar.
1 hectopascal = 100 pascal = 1 millibar
1 kilopascal = 1000 pascal

Various Pressure Values
10 Pa - The pressure at a depth of 1 mm of water
1 kPa - Approximately the pressure exerted by a 10 g mass on a 1 cm² area
10 kPa - The pressure at a depth of 1 m of water, or the drop in air pressure when   going from sea level to 1000 m elevation
10 MPa - A "high pressure" washer forces the water out of the nozzles at this pressure
10 GPa - This pressure forms diamonds

Alternative Units of Pressure
1 bar - 100,000 Pa
1 millibar - 100 Pa
1 atmosphere - 101,325 Pa
1 mm Hg - 133 Pa
1 inch Hg - 3,386 Pa

A torr (torr) is named after Torricelli and is the pressure produced by a column of mercury 1 mm high equals to 1/760th of an atmosphere. 1 atm = 760 torr = 14.696 psi

Pounds per square inch (psi) was common in U.K. but has now been replaced in almost every country, except the U.S., by the SI units. Normal atmospheric pressure is 14.696 psi, meaning that a column of air on one square inch in area rising from the Earth's atmosphere to space weighs 14.696 pounds.

The bar (bar) is common in the industry. One bar is 100,000 Pa, and for most practical purposes can be approximated to one atmosphere. 1 Bar = 0.9869 atm. 

There are 1,000 millibar (mbar) in one bar. The unit is common in meteorology. One millibar = 0.001 bar = 0.750 torr = 100 Pa.