I'd say conceptually, you could think of the internet as consisting of 2 parts, nodes and links. A person's computer would be an end node; webservers that host things like this website would be somewhere in the middle of the web of nodes.
For example, here is a relief sorta deal that shows geographically where the most important links and nodes lay. The peak areas would be high usage. Of course this is just a fiber optic pathway, not the complete internet:
Here are some telecommunications "links" that run under our oceans (submarine cable):
Here is a picture detailing the physical links of an internet "backbone" UUNET. This is one of many of our internet backbones:
Another conceptual picture from the ANS/NSFnet T3 backbone:
One thing, those nodes you see in the center are huge, critical nodes to the internet's functioning, not someone's household computer. Also, there are many nodes not visible here, the ones that you must go through before and after the backbone.
The internet backbones are sorta like taking a ride on the train. You use it because it's fast, but unless you're lucky it doesn't stop right outside your door. First you have to walk to your car, drive to the train station, get on the train (now you're really moving), but then get off at your stop, hop on the bus, take a walk, and you're at your destination. Towards the beginning and ending of your trip, you have to jump through a lot of little geographically specific nodes to get to the train station, but once on, you're moving together with everyone else.
As for the "nodes" I mentioned above, they are just servers and computers spread across the world in government buildings, internet server farms (places where you keep a lot of servers), businesses, universities, and even people's homes. Each node has it's own 4 number, 3 digit address, even ones that are named, like for comebackalive.com its 205.234.206.226.
An example of what a server room in a university or business might look like (wherein there are servers that people can access from the internet):
While a server farm, located inconspicuously in big cities everywhere, looks more like:
and
With most operating systems, you can actually see a textual representation of the path that your data takes as it goes between you and a destination. the command "tracert" will show you the number of nodes, the name of the nodes, and how long it takes to get to each node.
So, if I do a "tracert comebackalive.com", which maps the path from my comp to this website, it returns (starting from the 3rd node for security reasons):
Tracing route to comebackalive.com [205.234.206.226]
over a maximum of 30 hops:
3 20 ms ge-1-1-ur01.ogden.ut.utah.comcast.net [68.87.170.249]
4 20 ms te-9-1-ar01.saltlakecity.ut.utah.comcast.net [68.87.170.21]
5 11 ms te-9-3-ar02.saltlakecity.ut.utah.comcast.net [68.87.170.6]
6 23 ms COMCAST-IP.car2.Denver1.Level3.net [4.79.82.54]
7 24 ms te-3-3.car2.Denver1.Level3.net [4.79.82.53]
8 35 ms ae-32-54.ebr2.Denver1.Level3.net [4.68.107.126]
9 53 ms ae-3.ebr3.Chicago1.Level3.net [4.69.132.62]
10 50 ms ae-78.ebr2.Chicago1.Level3.net [4.69.134.61]
11 51 ms ae-23-56.car3.Chicago1.Level3.net [4.68.101.167]
12 49 ms 261.xe-0-3-0.cr2.ord1.us.scnet.net [4.71.100.26]
13 51 ms 216.246.95.243
14 51 ms 216.246.94.202
15 49 ms 205.234.206.226
Trace complete.
The first number is the sequential node enumeration (or "hop"), the second is the amount of time that trip takes in milliseconds (aka "ping), the third field is the server name. Fortunately, lots of server names have geographical info. So you can see first my data traffic goes to ogden (20 minutes north of me), then it goes to SLC (20 minutes south of me) then it heads to denver, then it heads to chicago. From there, it heads to "scnet.net", which, if you go to the webpages "http://www.scnet.net/", you find out its a datacenter/serverfarm in chicago. It looks like our comebackalive.com would be found within the serverfarm of that company, which might be below their office building or grouped close to other servers of other businesses in a completely different building.
So, well, hope that helps. I learned that comebackalive.com is in chicago!