Okay kiddo, so you know how cameras work, right? They use something called a sensor to capture the image. Well, a back-illuminated sensor is just a fancier type of sensor that can take even better pictures.
Think of it like a cake. The top layer of the cake is usually where all the decorations go, but if you turned the cake upside down, the bottom layer would be exposed. It's the same with a back-illuminated sensor. Normally, the top part of the sensor is where all the electronics are. But with a back-illuminated sensor, the electronics are moved to the back, and the front is left open to capture more light.
Why is this important? Well, when you take a picture, light enters the camera and hits the sensor. The more light that the sensor can capture, the better the picture will be. So with a back-illuminated sensor, since the front is open to capture more light, you get a clearer and more detailed picture.
It's kind of like having a bigger bucket to catch raindrops. If your bucket is small, you won't be able to catch as many raindrops, but if your bucket is big, you can catch a lot more. That's what a back-illuminated sensor does for a camera. It makes the "bucket" bigger, so you can catch more light and take better pictures.