Recall that the mean anomaly indicates the position within the orbit of the satellite/object. In the short term, whilst the other five orbital elements are only very slowly changing, the mean anomaly rotates by 360 degree for every revolution completed.
The significance of the mean anomaly in a TLE then is that it is telling us both:
(trivial answer) that the object was estimated to have that combination of mean anomaly at that given epoch. From this you can calculate forwards or backwards a little way and find the position of the satellite at other times.
(slightly more meaningful answer) that in the orbit determination effort data was gathered from a number of parts of the orbit, or consecutive orbits, and was decided to publish the TLE with that epoch. You can probably see that this is only slightly more meaningful in the sense that it could be interpreted as the centroid of that data collection effort though it wouldn't surprise me if the epoch is chosen to obscure any hints about the data collection sensors involved.
In isolation, without the whole orbit information, there is little that can be learned from the mean anomaly alone. The implication, assuming that the Iridium satellites you refer to aren't being wildly manoeuvred, is that the habitual choice of publication epoch chosen for each satellite varies: for some the mean anomaly changes more than for others as a result.