To see an outdated list of mail servers and routers.
For example, in Europe core1-gig2-0.bletchley.ukcore.bt.net is down. Sounds pretty "core routing" doesn't it? Shame that the DNS name doesn't resolve, so lets mark it as 100% packet loss shall we?
Hmm, maybe it's not packet loss at all...
The Asia link is reporting 2 routers in Iran down, and a name server down in India for an ISP which has 5 other name servers (which are not monitored by ITR), which are all up. Perhaps Iranian internet traffic is being filtered? I know there are a number of blockades around Iran at the moment.
Basically the source list is very poor and outdated, and the site itself should not be trusted.
The best sources are normally specific to one network, for example AT&T have a very informative network status page where you can select a US city and see network performance from it to other cities around the US and the world.
The way that particular website works is people submit routers to be pinged, they ping them every 5 minutes, and graph the results. That's it.
It's not in any way an accurate view of the Internet's performance as a whole.