1. What is traceroute?

Traceroute (or tracert in Windows) is a program that prints the route packets take to network host.*

2. What is the use of traceroute?

The Internet is a large and complex aggregation of network hardware, connected together by gateways. Tracking the route one's packets follow (or finding the miscreant gateway that's discarding your packets) can be difficult. Traceroute utilizes the IP protocol `time to live' field and attempts to elicit an ICMP TIME_EXCEEDED response from each gateway along the path to some host.*

3. How does traceroute work?

This program attempts to trace the route an IP packet would follow to some internet host by launching UDP probe packets with a small ttl (time to live) then listening for an ICMP "time exceeded" reply from a gateway. We start our probes with a ttl of one and increase by one until we get an ICMP "port unreachable" (which means we got to "host") or hit a max (which defaults to net.inet.ip.ttl hops & can be changed with the -m flag). Three probes (change with -q flag) are sent at each ttl setting and a line is printed showing the ttl, address of the gateway and round trip time of each probe. If the probe answers come from different gateways, the address of each responding system will be printed. If there is no response within a 5 sec. timeout interval (changed with the -w flag), a "*" is printed for that probe.*

4. How do you determine the location of the traceroute server?

*directly quote from manpage of traceroute.