Typical atmosphere near sea level, in ambient conditions is around 100,000 pascals.
But the pascal, as the unit, is not defined through Earth atmospheric pressure. It's defined as one newton per square meter. The newton is $\rm{kg \: m}\over s^2$. So, $\rm[Pa] = [ {kg \over {m \: s^2}} ]$.
Nowadays, definitions of units are often fixed to various natural phenomena, but it wasn't quite so when they were being created.
The Second is an ancient unit, derived from a fraction of day, 1/86400
of synodic day on Earth. The meter is derived from circumference of Earth, $10^{-7}$ the distance from north pole to equator. The kilogram came to be as mass of a cubic decimeter of water.
100,000 pascals, or 1 bar, though, is about the average atmospheric pressure at sea level. That's an awfully round number – while Earth atmosphere pressure doesn't seem to have anything in common with the rest of the "sources" of the other units.
Is this "round" value accidental, or am I missing some hidden relation?
Best Answer
This is a coincidence. There's nothing about the atmosphere that would make it have a nice relationship with the Earth's rotation or diameter, or the fact that water is plentiful on the surface.
On the other hand, it's important to note that the coincidence isn't quite as remarkable as you note, because of a version of Benford's law. Given absolutely zero prior knowledge about how much air there is in the atmosphere, our guess about the value of the atmospheric pressure would have to be evenly distributed over many orders of magnitude. This is akin to throwing a dart at a piece of log-scale graph paper:
Note that the squares in which the coordinates start with $1.\:{{.}{.}{.}}$ are bigger than the others, so they're rather more likely to catch the dart. A similar (weaker) effect makes the probability of the second digit being 0 be 12% instead of the naive 10%.