If you look at the letter behind the flight number it's really the class designator of the paid fare. It provides you with a specific amounts of Avios and tier points.
The paid fare class is also decisive if you could use Avios as an upselling instrument. E.g. the German version of the Terms and conditions of the Exec Club show:
"Upgrades mit Avios Punkten sind nur bei entsprechenden British Airways Tarifen möglich (gültige Buchungsklassen sind: J, C, D, R, I, W, E, T, Y, B, H)."
Therefore this designation/letter is decisive for some services within the same travel class.
If you look at flightstats.com and the flight availability you can see also not only the four travel classes ranging from First through Business and World Traveller Plus to World Traveller but also the number of available seats.
The M availability as a higher fare bucket should be (normally) higher than those of the special discounted fares.
So a booking
BA0903 M 14AUG will result in the same cabin as
BA0903 S 14AUG
FRA -> LHR. All are Economy Class fares
Hope this helps.
Hmm but then why the "M" appears on the boarding pass when I book into a fare bucket not M?