Dimension reduction is like taking a big box filled with lots of different things, and reducing it to a smaller box with just some of the things. Let's say you have a big box filled with colorful balls. It has five different colors, red, blue, green, yellow, and orange. This box has five "dimensions" or ways that the balls can be sorted - by color.
If you wanted to reduce the size of the box and the number of things inside it, you could pick just three of those colors, for example red, blue, and green. This smaller box would now just have three dimensions or ways to sort the balls by color. This is an example of dimension reduction.