first hand experince
basically, as stated prior, it is the different mixes of aluminum alloys that make up the frame of the bike, and yes these are proprietary gimmicky names given by specialized. a1 it was pointed out that may be the equivalent of 6061 aluminum. As specialized has perfected alloys they have been able to, over the years, create lighter, stiffer alloys, thus the m4 and m5 designations. I owned a 2008 stumpjumper, m4 aluminum, which was substantially lighter than the 6061 aluminum that lesser models are made of, I upgraded to the 2010 stumjumper which is m5 and it is quite a bit lighter, maybe 5 pounds or more, yet just as stiff and durable. specialized also grades their carbon in a similar way, 8r,9r, etc.,
in reading up on the innovation, each step up is a little lighter and a little more durable, so they are able to make the same frame, a1 vs m5, and not only use lighter material but also use less of it, creating a substantially lighter bike each time.
Gimmicky or not, (and I am sure each manufacturer does something similar), I am very happy having gone to newer versions of both my specialized mountain bikes and my road bikes.
The higher the grade with specialized denotes both weight and quality of the material used to produce the bike. I do believe at this point, 2014, even the aluminum bikes purchased at walmart are of the 6061 aluminum, (aka, a1, I am assuming). Don't be afraid to invest a bit more into a better, lighter, stiffer alloy.
Don't take the internets word for it, visit your local bike shop and try some bikes at different price points. With any purchase, decide where quality meets your budget, (or check the used market as I have, there is honestly no way I would have been able to afford a new $2000 mountain bike or a $3500 road bike, just know what you are getting before you're ready to lay out $1-1.5k or more on a used bike, and maybe have the desire to do some maintenance on your own, as some repairs are simple and bike shops make some bucks on service). Both bike I currently own were bought used with very little use, as some people buy these bikes to get into the sport then realize its just not for them.
Speaking of service, I was able to invest in a basic Park stand and most of the common tools to service my bikes for less than $400, I figure that's about 3 years worth of tune-ups and brake service for two bikes, and I can do the work myself indefinitely.