Caliber is the measurement of the rifle bore diameter.
I suppose for a bullet, in the US I think it is the diameter of the bullet in hundreths of an inch.
For the most part, this is approximately correct. However, manufacturers take a LOT of liberty with naming specific cartridges.
The .32 H&R Magnum has a bullet diameter of 0.312", or .31 caliber.
The .38 S&W Special is actually 0.358" (lead slug measurement), so that's basically .36 caliber.
The .44 Special and .44 S&W Magnum measure 0.429", or .43 caliber.
There are many
many other cartridges with similar deviations from TRUE caliber measurement.
Interesting, historically "caliber" was not a bore designation of hundreths of an inch, but rather a ratio of diameter to total barrel length.