Hydraulic systems, such as lifts, airplane controls, and brakes often use MPa to communicate pressure and tensile strength values.
For example, the pressure in a steam locomotive is around 1 MPa, a pressure washer generates around 10 MPa, 25 MPa is a typical diesel brakes system.
400 MPa is the chamber pressure inside a machine gun.
Applications In Health
Dentists and medical professionals use MPa to communicate tensile strength of cured resins for tooth and bone repair.
Your chipped front tooth needs to withstand the pressure of 1 MPa, or about 145 psi.
The dental crown of your back molar needs to withstand much, much more. The resin used for your back teeth must be rated to withstand 6 MPa, or about 900 psi.
Applications In Engineering
Construction and tank manufacturers use MPa or ksi to communicate tensile strength for platforms or tanks. Correct calculation of objects under load is critical to safety.
Recent high profile bridge collapses in Florida and Genoa, Italy put engineering documents into the spotlight. The news media is rife with speculation that engineering flaws caused the collapses.
For more information on practical uses of MPa and pressure scales, several engineering publications and industry guides are available.
Try looking at sensor manufacturers and construction documents for more real-life examples.