Series of tubes is a good analogy, but it's not complete.
Really I feel that any person able to function in society should be able to understand this:
Computers use electricity to do mathematical operations, and store and transmit information. This information can be represented as numbers, words, images, audio, video. For children, use this opportunity to show a record to demonstrate how audio relates to vibrations, and movie film, to show how video is a series of still images.
Computers use electricity to do math. They can do this extremely fast. Everything that a computer does is based on a series of mathematical operations. A computer is able to do so much math so fast that it can perform extremely complex feats using simple math as a building block. To a computer, it is not very important whether the math represents words, audio, or video.
These electrical signals can be sent over great distances, like a telephone or telegraph. Use a battery, wire, and a lightbulb/LED to show a telegraph, and a laser pointer and fiber optic cables to show light being used to send the data. Show a cellphone and FM radio and explain briefly that radio waves can be used as well.
Two computers can send information between each other in this manner. In fact many computers can be connected to each other, to send information between each other over great distances. This is the Internet. Instead of this battery, wire, and lightbulb, we have millions of computers interconnected with countless wires. This interconnectivity gets very complicated, but to the computers involved, they are simply repeating simple math very quickly.
When you look at a web page on the Internet, whoever wrote the words you see did it on a computer that turned it into numbers. Whoever took the pictures you see did it with a camera that turned it into numbers. Whoever recorded the sounds you hear did it with a microphone that turned it into numbers. It was sent to you through a series of computers, transferring the numbers using electricity, light, or radio waves. For your computer to show it to you, it used the numbers to turn it back into light on your monitor. (Optionally explain speakers, it's a bit of a tangent but you can involve the telephone and some history).
This should make sense to anyone. You can elaborate by drawing a simplified diagram of routers and hosts, and also explaining storage with the record as a starting point. The routing of packets is easy to explain - each computer has a numerical address. For any address, each router knows what direction it is in.
The real issue is that most people don't want to understand. They don't want to spend a few minutes of their day learning something. The education system in the developed world is designed to remove people's will to learn. It's not that people can't understand such simple concepts. You simply can't convince them to listen. For people who are willing to listen, it's easy to help them understand. My experience is that this means very young children, and old people who have a technical background. This is similar to the problem of people who refuse to read what's on their computer screen. Software meant for end users that does not work based on reading the screen and answering the questions is broken. There's a lot of broken software out there. But also, a lot of people simply refuse to read the screen.