Headphones, like dynamic loudspeakers, present a complex impedance load to an amplifier. Depending on the frequency of the signal being passed, the instantaneous impedance can be either resistive or reactive.
A simple impedance graph will typically have one or more sets of peaks and dips representing maximum and minimum impedance values for the driver across the audio spectrum. The maximum impedance usually occurs at the driver's resonant frequency(s). The minimum can occur at any frequency.
The same data displayed as a complex impedance graph would look like a series of concentric circles, often with tight little loops. Where the circles cross and touch each other corresponds to the resonant frequency of the driver. The X-axis (measuring frequency from 0 - 20,000 Hz) separates the resistive component from the reactive one. Any value above the X-axis is positive and is a resistive load, any value below the X-axis is negative and is a reactive load.
A few loudspeakers, and headphones, present mostly a purely resistive load across the audio band. If you go to the website of HeadRoom Corp. at
www.headphone.com, they have simple impedance curves for many popular headphones that you can display.
Generally, speaker drivers that present mostly resistive loads are easier for an amplifier to handle as there is no back-EMF signal present at the output terminals for the ampflifer circuits to deal with. This may not be a real problem with headphones, but it definitely affects the sound of certain speaker/amplifier combinations.
Your multimeter presents a DC signal to the speaker, something which would never happen when connected to an amplifier. The nominal impedance value you read is probably somewhere between the minimum and average value, but not the maximum impedance value.
Low level DC current such as your meter provides probably won't hurt your phones. Higher current levels from a larger battery like a 6 volt lantern battery or a brute like a 12 volt car battery would probably overextend the driver and quickly overheat the voice coil, ruining the phones.