A bar is a unit of pressure. A millibar is one-thousandth of a bar.
For reference, the following are all ways to write the air pressure at sea level in different units:
1 atmosphere (atm)
1.013 bar
1013.25 millibar
101325 pascal (Pa)
14.696 psi
760 mmHg
As for why we have so many different units to choose from, it depends on the thing we want to measure and historical context. Measuring the outside air pressure in pascals is impractical since the numbers are big. For example, you wouldn’t want to measure the distance to the store in centimeters. bar, millibar, and pascal are all metric units, which are the standard in scientific fields. psi is often used in imperial countries for pressurized objects.
I’m not a meteorologist, but generally a region with lower than normal air pressure is likely to develop bad weather. Air flows from high to low pressure (wind) so any clouds that wind picks up is pushed towards that area of low pressure.
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