That's the way to measure the current flowing through the circuit, set your meter to the amps function, and 200mA or maybe 20mA.
The meter can be put into any of the wire connections and still read the same current. The same current flows through all components in the loop.
Note the meter will drop a small voltage, perhaps up to 200mV, which will reduce the current flowing slightly. You can estimate the current by measuring the voltage across the resistor (using the DMM on voltage), and using Ohm's Law. Obviously this depends on the accuracy of the resistor for the conversion to current, but it avoids the voltage drop of the meter on its current range. While the meter will take a little current, this method of connection will disturb the circuit far less than the current connection. It also means you don't have to break the circuit to estimate current.
One further, very important (for me) point is that your meter stays on the volts setting. If I put my meter on current, it tends to stay there until I next try to measure volts, and probably kill it. Always take your meter off current after using it to measure current!