A traditional oscilloscope works in almost exactly the same way as a traditional (cathode-ray tube) television; indeed, you'll sometimes see oscilloscopes referred to as cathode-ray oscilloscopes or CROs. In a TV, electron beams are made to scan back and forth across a screen coated on the back with special chemicals called phosphors. Each time the beam hits the screen, it makes the phosphors light up. In less time than it takes to blink an eye, the electron beams sweep across the entire screen and build up the picture you can see. Then they do it all over again. And again. And again. So you see a moving picture instead of a still one. (Take a quick look at our television article for a diagram showing you how all this works in practice.) In an oscilloscope, the electron beams work the same way but instead of building up a picture they draw a graph. When you watch a line being drawn on an oscilloscope screen, what you're actually looking at is an electron beam wobbling up and down!
Here's something to note: the electrical signals feeding into the x and y connections effectively become the x and y values on your on-screen chart. Since there's a one-to-one correspondence between these two things, a traditional oscilloscope is an analog device. (Another way of looking at it is to say the trace on the screen is an analogy of the thing you're studying or measuring.)