what the hell is this site, and how does it relate to the security of my bitcoins?
I'm not sure what the purpose of that site is, unless it's a joke. It isn't a database (that would be impossible), it's generating the pages in response to queries. So possibly an attempt at a scam, as in you look for your private key, and the holder of the list uses the generated pages to narrow down the possible addresses that have actually been used (there are 2^160 possible addresses, or 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976). Since people have trouble putting that in perspective, there are only 2^63 grains of sand on all the beaches of Earth.
The total number of bitcoin addresses in use is so much smaller than the amount of possible addresses, that something like this is completely and utterly useless, and it would also be trivial to expand the number of possible addresses in the future. I laughed when I saw that website, cause I just know people who don't know the math are furiously putting page numbers hoping to find one
. You'll likely witness the heat death of the universe before that happens. 
