BGP looking glass is used to look at the state of the public prefix on the internet. It could also be use to verify if the route announced by my Internet Gateway router is visible on the internet. In addition to this, I can also use a BGP looking glass or a route server to trace the traffic to my network as well. Say for eg: Below is the topology.
|| INTERNET ||
// \\ /// \\\
| ISP1 | | ISP2 |
| | | |
\\ // \\\ ///
| Internet GW |
Considering a hypothetical scenario consider that your ISP GW is announcing routes to the two ISPs - ISP1 & ISP2 in a manner that traffic from US & Europe needs to come in Via ISP2 and Traffic from ME & Asia needs to come into your network via ISP1. Ofcourse you need to go through the Peering links of the respective ISPs to understand the BGP communities you would require to fulfill this requirement.
Now, if you want to verify if the incoming traffic coming from US & EU is entering your network through ISP1 then you would be required to login to a BGP looking glass or a route server from the US & EU regions and do a trace from there to your network prefixes to see if the traces reach your network through ISP1. Also, if you would want to verify if the traffic coming from ME & Asia you need to login to the BGP looking glasses of those regions and do a trace to your network to verify if they are taking ISP2 to reach your network. This is just one of the uses of BGP looking glass or a BGP Internet route server.
I hope it helps.
And here is link for lookin glass provided by NIXI:
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