This is not a question or even tutorial, it's just for those who are curious about how the "Internet" really works, and possibly could be a sticky thread. This is a basic explanation and diagram.
How you see websites
So basically, you are connected to your router (of course). When you open your web browser and then type in bleepingcomputer.com for example, your PC sends a request through your router to your ISP, who sends a request to the DNS server. The DNS server translates the address you typed in to a computer-friendly IP that will take you to the website. Then they redirect you to the server's ISP, then to the actual web server. They return the homepage html and css, which goes back through your ISP, DNS server, and router back to your PC.
Why some websites load faster than others
Although you may have some crazy-fast 100mbps Internet connection, that's actually a measure of how fast the connection is just between you and your ISP. A certain website may only have a 10mbps connection to their ISP, for example, so they can only send data that fast until it reaches your ISP. After it does, it'll come at full speed. That's why Google loads way faster than most other websites.
Why multiplayer games need a moderately fast connection to be playable
They update the positions and sometimes the physics of each specific player (and in Minecraft, block states and many other things) so you can see them on your screen smoothly. If your speed is too slow, that update will not be frequent enough, and you will experience lag.
Here's a simple diagram of how you see websites:
From here. Diagram used under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license. Thank you for reading! This article (except the diagram) was created with 100% of my prior knowledge. Tell me if I have something wrong or I need to add something.
Edited by gigawert, 14 July 2015 - 06:01 PM.