A tone reproduction curve is like a magic wand that can turn a digital image into something that looks like real life. When we take a picture, the camera has to compress all the colors and brightness levels into a limited number of pixels. This means that some of the subtle differences between the lightest and darkest parts of the image can get lost.
But with a tone reproduction curve, we can tell the computer how to spread out the colors and brightness levels in a way that mimics how our eyes see things in real life. Imagine you are coloring a picture with markers, but you only have a few colors to choose from. You might use the lightest color for the sky and the darkest color for the ground, but what about all the in-between shades? You could use the other colors, but they might not look quite right.
Now imagine you have a bigger set of markers, with many more shades of each color. You can use these to create a more realistic picture, with smooth transitions between the light and dark areas. That's what a tone reproduction curve does – it gives the computer a bigger set of colors and brightness levels to work with, so your image will look more true-to-life.