What does it mean to be remembered?

"But the thing about remembering is that you don't forget." - Tim O'Brien from The Things They Carried 

     While this quote seems incredibly simplistic in its literal translation, I think there's a great deal more to it than the obvious definition it states. Of course remembering implies that you don't forget; isn't the whole point of remembering to be able to recall the past and not forget it? What really gives this statement meaning is when we start to think about what it means to remember and be remembered.
     It seems as though everyone has some idea of how they want to be remembered, although often times these expectations are far from realistic. A lot of people dream of going on to make an impact and change the world during their lives, and hold the assumption that global recognition is the key to being remembered. While I don't intend to crush anyone's goals in saying this, it just isn't statistically possible for every person to be remembered on that level, but I don't think that makes anyone's memory any less important. It can be difficult to not feel insignificant in this world of seven billion people, but even so, everyone still has an impact. Maybe I'm interpreting this quote on a completely different route from it's intended meaning, but the way I see it, the important thing is recognizing that being remembered doesn't have to mean being remembered by millions. The important thing is recognizing that even if you can't see it, the little things you do make a difference to somebody, and those that are closest to you will never forget how you touched their lives.