Like roads with intersections, the Internet is made up of cable and fiber, where the intersections are controlled by routers. Aptly named, routers decide which route is least costly and send data packets in that direction. A trace route verifies the route a packet takes to reach its destination. This is useful for determining whether a router has failed. If the command is unsuccessful, you can determine where routing failed, possibly indicating router problems.
Trace route is also useful for determining a slow router.
The response time is returned in the output, indicating the effectiveness of a router. This is set to some suitably high number. As this packet moves through the route to the destination, this number is decremented by 1. Trace route plays with this TTL number on outgoing packets. It first sends out a packet with a TTL of 1.