latest Sci Show Kids episode explains in simple terms how computers work. The video contains fine explanations for elementary school students albeit a bit too fast-paced for my liking. Watching the video sent me on a quick search for more video lessons about how computers work.
The first place that I looked for a video about how computers work wasn't YouTube, it was Common Craft. Common Craft offers a video lesson on computer hardware and one on computer software. Both videos are appropriate for students of middle school age or older.
TED-Ed offers a couple of lessons on how computers function. The first, embedded below, covers how a computer's memory works and its function within a computer. The full lesson can be found here.
The second TED-Ed lesson on this topic explains how all of the parts of your computer work together to generate what you see on your screen.