If you think of the various lines connecting all the different servers on the Internet as being a network of freeways, it becomes easy to see how even though the route you're taking to get from point A to point B may be blocked, others can reach point B because they're taking a different route.
I once could not reach my own websites, which reside on servers in New Jersey, but I could go everywhere else on the 'net. I was on the phone with a friend, discussing one of my sites, and he could see it just fine. So, I fired up the old copy of AOL I have on my machine and tried connecting that way - bingo! I was in. But I still couldn't reach it through my broadband connection. So I ran a trace route through my broadband connection and one through AOL. You guessed it - even though both originated from my machine, AOL was using a different route to get from Orange, CA to New Jersey. In fact, the trace route from my broadband connected died in Memphis, TN. It turned out that a Sprint Communications owned switch somewhere in Memphis had gone bad and was effectively blocking traffic. I called tech support, discussed the problem, they called Sprint, and within two hours it was fixed and working. The websites in question were never really down, I was just stuck in traffic so to speak.