A current metrr has a small resistor inside. Depending on the range you choose (or autorange), the retsitance may be small or larger.
The meter then measures the voltage over this resistor. That value is used to calculate the current through that resistor (which is equal to the current through your circuit).
Measuring current may quite easily damage your stuff or your meter (as it has near zero resistance, currents may get quite high).
In the high amp range, the resistor may be 0.1 ohm, in micro amp range, the resistance may be 1 kOhm or more. All depending on the quality of your meter.