For physical constants, weights, and measures, there are known and agreed values in the International System of Units (SI). Such constants include the length of the meter, the mass of the kilogram, and the volume of a liter.
In the USA, a governmental organization called the National Institute of Standards and Technology maintains standards and is considered the arbiter and ultimate authority for values of SI units and industrial standards. NIST also defines traceability, by which an instrument's accuracy is established in an unbroken chain relating an instrument's measurements through one or more derivative standards to a standard maintained by NIST.
Please add references to standards organizations in other countries. Other definitions and/or views on traceability also welcome.
Please add mention of instruments that are commonly calibrated. A discussion of statistical error would also be appreciated.