First off, the definition of provisional marriage.

The name "marriage" was given by the General Headquarters.

How people actually take it differs from base to base.

In some bases, they seem to treat it like the literal marriage.

Anyway, what it actually does in all cases is "Freeing the limit of expertise" of us shipgirls.

Simply put, it's removing the level cap.

More specifically, the rigging core gets fitted with a new system that removes the level cap and enables upgrades of equipment performance.

I guess it's comparable to upgrading CPU or RAM in computers?

↑ Berserker

Which means surgical enhancements are necessary one way or another.

I've received a ring after the procedure, but does it matter?

That would depend on the base... or rather, the admiral posted there.