Overpressure is just the pressure in one location is higher than in the surrounding media.
Tanks have an NBC( Nuclear, biological, and chemical) protection system. They work by having incoming air going trough a filter system that stop the bad stuff from passing through just like if you use a gas mask. Tanks are not air tight so air could com int from the outside in many location. To stop that from happening the filter system has fans that pressurise the inside of the tank to slightly higher pressure the the outside. This means in gaps air will only escape.
There are protective masks for usage when you work with volatile chemicals that has a filter and a fan on you back. Ther is then a pipe that blows into the mask you have around your head where it can escape out. The pressure the fan creates stops air from leaking in around your face. That is quite close to how the NBC system and overpressure works
In regards to explosives, overpressure is the pressure of the shockwave the explosion produces above atmospheric pressure. An explosive is fundamentally the creation of a high-pressure gas that will then expand to even out the pressure. The force from the gas that escapes is high enough so it can damage stuff and kill peopel
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