What does a calibrator actually do?
As stated above, a "Calibrator" is indeed a device used to calibrate another device.  There are many types though.

(The below only deals with Voltage as per the original question)

A Primary Standard is a standard based on absolute, immutable physical properties of a system.  For voltage, they typical primary standard is a Josephson Junction Array.

A "Working" or "Secondary" standard is typically a high precision voltmeter, with very low drift over time or temperature characteristics.  Even so, they are designed to work only over a limited temperature range.  Working standards are usually guaranteed to maintain their calibration over a certain period of time, anywhere from one week to several years.  Instrument manufacturers generally target 1 year.  Working standards need to be calibrated on a periodic basis to either a higher precision working standard, or preferably a primary standard.

In the USA, a Working standard is typically calibrated on a periodic basis to an NIST (National Institute of Standards and Technology) traceable source.  That means the calibration can actually be traced back to a certified primary standard.

The Working Standard is what an instrumentation tech would typically use to calibrate an actual field device.

Just a note, that all 'Field Calibration' references need to be calibrated or at least checked against a primary source.  Even something as simple as weights used for calibrating scales.  Over time, the actual weight can change just from absorption of atmospheric gasses.  When a lab checks a purely physical standard, they don't generally modify it to make it equal to the reference.  For a mass (weight), they will not typically add or remove mass, rather they will issue a certificate that states what the actual mass of the object is.