If are measuring current in a series circuit with a multimeter and get a reading of 0.01 mA what does it mean?

0.01 mA is 0.00001 A. This is the current required to develop a voltage of 0.01 mV across 1 Ohm. Since it is a series circuit, it is also true that the current on 0.01 mA is present at every point in the circuit.