Slash chord, „m7 over ”. On the left side of the slash you can see a chord, on the right side the lowest tone (bass).
The m7 chord consists of the tones  (1), [m3] (m3),  (5) and  (7). As you can see, the bass  is part of the basic triad of the chord. The bass on the right of the slash does not necessarily be part of the chord symbol on the left, except the bass is part of the basic triad. In this case it wouldn't make any difference, since even without the 5th the chord on the left would be written as m7/
You can find the m7/ chord in the same situations, where a [m3]/ or [b6]maj7/ could be written. If you read one of these two chords, you can often replace them by a m7/. Let's take a closer look at the two chords:
[m3]/: the m7 chord can also be seen as [m3] major chord over the root . That explains, why you can find the m7/ chord in the same situations, where you might expect a [m3]/ chord. Actually you could even write the m7/ chord as [m3]6/, in which the  is the 6th of the [m3]6 chord. For better readability of a chord chart you might consider the  as just a melody tone and just notate a [m3]/ chord. Be careful: contrariwise the [m3]/ can not in all cases be replaced by a m7/, because the  that wil be added by doing so might not always fit.
[b6]maj7/: if you like the positive character of the sound, you can nearly always add a 9th to a major chord or a maj7 chord, turning them into an add9 repectively maj9 chord. By playing a [b6]maj7/ chord and replacing it root [b6] by 9th , you end up with the same chord shape as the m7/ chord. Thus, you may interpret the m7/ chord as [b6]maj9/ respectively [b6]add9/ chords, that is played without its root [b6].