Traceroute is a command which can show you the path a packet of information takes from your computer to one you specify. It will list all the routers it passes through until it reaches its destination, or fails to and is discarded. In addition to this, it will tell you how long each 'hop' from router to router takes.
In Windows, select Start > Programs > Accessories > Command Prompt. This will give you a window like the one below.
Enter the word tracert, followed by a space, then the domain name.
The following is a successful traceroute from a computer in London to wesh.co.uk:
Firstly it tells you that it's tracing the route to wesh.co.uk, tells you the IP address of that domain, and what the maximum number of hops will be before it times out. Next it gives information about each router it passes through on the way to its destination.
Each of the 3 columns are a response from that router, and how long it took (each hop is tested 3 times).
If you have a website hosted with us (Or elsewhere), it would be a good idea to do a traceroute to it when it is working, so that when it fails, you can do another traceroute to it (which will probably time out if the website is unreachable) and compare them. Be aware though, that it will probably take a different route each time, but the networks it passes through will generally be very similar.
If you ever encounter problems where your website is un-reachable, its advisable that you carry out a traceroute first to see exactly where the problem may be, as more often than not, the problem lays with either your internet provider, or your own router/modem, but if thats not the problem, then please be sure to grab a screen shot of your traceroute and attach it to a new helpdesk ticket for us to see.