His death represents the end of an era really. There is a reason people don't get excited about space exploration anymore, it's because we don't explore space anymore!
After the apollo 13 disaster, NASA and the american public went chicken on us. Since then people don't go anywhere in space. Yeah the ISS has people in it, but it's just in orbit. I equate that to traveling halfway around the globe for the super bowl and just staying in the parking lot once you get there. The mars probes and stuff are nice, but if you don't send people then it doesn't really count.
There were a lot of bad things going on in america back then, it really wasn't the simplier "better" times that many people claim it was, but one thing we did have going for us, was that the nation could rally together for the sake of dreaming. With the tech we had back then, putting a person in space, much less the moon should have been impossible, but America, as a nation decided that we would spare no expense and waste no effort in trying anyway. And guess what? It turns out that if you can get enough people behind something, the impossible IS possible.
If we as a nation and we as citizens of this planet could only unify ourselves again, like we did back then, it would be possible to fix all of the massive problems facing us today. I am regretful that I was born into a generation that will probably never have this sense of unity.
So to me Neil Armstrong is more than just some guy that rode to the dead rock revolving around us and back again, he symbolizes a point in our history when anything was possible. A time that I genuinely hope will come again. He will be missed.