Means normal. As in everything is as normal as the existence of rain.
But there's a dissenting opinion. I did a google search and came up with this. I'm nopt certain whether I accept it, but it's out there. I also laooked up right in OED -- goes on for pages, and I scanned quickly without coming up with right as rain.
Consider the phrase “right as rain”. Someone might say, “I felt like
the sun was going to come out, and I was right as rain.” Aside from the
mixed metaphor, why “right as rain”? What does correctness have to do
with rain? Nowadays in the English language “right as rain” is a kind
of opaque cliché. Perhaps its basic meaning can be expressed as
“straight as rain”, or “straight as rain falls”, aside from effects
winds may have. Years ago, people used to call straight lines in
English “right lines”, derived no doubt from the Latin linea recta, the
term once in common use. The words “right” and “recta” appear to have
come from an Indo-European root which means “to move in a straight
line.” The metaphor plays on a resonance between geometric straightness
and correctness of judgment. The basis for this metaphor appears to
have been propagated by way of Indo-European languages for thousands of
years. It seems to work by virtue of some underlying, hidden process
that takes place when we acquire an Indo-European language.
