[morzh]

as Dale has noticed, with some explanation:

The clamp is the core, making a current transformer.
It has to clamp around ONLY ONE wire (not, for example, the whole AC cable, as summary current will then measure Zero Amps). This one wire is the Primary winding of that transformer.
Inside the meter is the second winding, a milty-turn with Ohmic low-value load.
This is where the Voltage measured across that load as the proportional value to the current in the wire through the clamp. Then it is calibrated to show the Amps.

This is for the AC component.
If the clamp is DC-capable, the DC is measured by a Hall element.

In order for the transformer to work (that is the flux to circulate in the core) the clamp has to be closed. Else there is no core, no flux and no measurement.