So I could bore you all to death with this one!
After my first degree, the second project I did was a problem of dielectric breakdown - when it shouldn't have - basically an impulse simulating a lightning strike ~175kV on 24kV switchgear causing the air chamber to break down!
Anyway, traditionally the breakdown of insulation was measured in volts per mil giving a figure around 760V/mil however these days we would use kV per mm so air is around 3kV/mm.
At this point the air breaks down causing corona discharge - the blueish glow, and the ionising smell.
It is dependent upon air pressure and humidity, but not massively - in fact moisture can increase the dielectric strength.
The field strength is very dependent upon shape - sharp points concentrate the field and you get corona at lower voltages, hence the use as much as possible of smooth rounded shapes to shield any sharp points.
In wet conditions parts of the insulators become conductive (see below) this brings more sharper points (the edges of sheds especially) closer to each other electrically and increases the field strength, so more sharper corona, more ionised gas, and more partial discharges. (A partial discharge is where the field is sufficient to cause a sparkover between two points, but it doesn't spread over to the full extent )
Corona in itself does produce losses, but little more. However if the corona causes sufficient ionised gas that this ionised gas (which is conductive) gets close enough to earth, the corona at another point, or the corona of another phase - you can get a sparkover (NOT a flashover!).
EHV lines normally run at around 3kV/mm - that doesn't dictate the spacing because the field strength is not linear. Instead the spacing is a statistical calculation based on the swing of the line, the likelihood of 'streamers' of ionised gas linking up, birds flying between etc etc.
In terms of the insulators the field is distributed unevenly over the surface, and if just a straight piece should this get dirty then combine this with moisture and you get a conductive path - in which case the non-conductive spacing along the surface can't withstand the voltage and you get a flashover.
(Flashover is along an insulator, sparkover is through a gaseous medium).
So to keep this at bay, cup or bowl shaped shed insulators are used - the idea being that the underneath bit remains less dirty and dryer to actually provide sufficient surface length - ignoring the wet/dirty exposed portion that may act as a conductive surface. On lower voltages instead of sheds the surface is extended by wavy shapes for the very same thing.
Obviously dirt can still build up too much, and they have to be washed down to limit this build up.
I always assumed the sheds were called sheds as they are in effect like a roof over an open shed - probably using bowl or cup implies such a specific shape that it doesn't suit everything.
Edit
I should add the statistical calculation is defined in iec61472.
I will see if I still have it, I cleared a lot of my stuff out when I "retired"