I don't know what it means to anyone else when they say it, but when I say "My name is Eddie and I'm an alcoholic" I am acknowledging that though it's been a decade since my last drink I am convinced that one drink will lead to the next, and ultimately (likely in a matter of days, not months) right back to the night I considered the relative merits of suicide versus sobriety.
I still go to several meetings a week (at least two, and often four) and I understand that at times meetings may seem unnecessary. But I usually feel far more grounded after even *meh* meetings and I've seen way too many folks stop working their sobriety and meander back to where they started. If you need a change, make a change - but do it with eyes wide open and conscious of what you are changing TO rather than FROM. TO is where you are heading, and where your future happiness lies - don't leave that to chance.