Later layers are learning patterns from the previous layer, and the patterns that each layer learn may stack on each other, so layer 3 is learning the the pattern that layer 2 is learning from layer 1 which is learning from the raw image, for example.

More complex patterns are learned by the later layers as they build on the simpler layers from early on. For instance, in a facial recognition model, early layers may learn to identify horizontal and vertical lines, mid layers may identify circles, and later layers can find eyes, noses, etc.

The main idea of a convolutional neural network is to take an image and convolve across the pixels with a filter. The values of the filter (which is some NxN matrix) determine what the potential shape represented in an image. You take the output of the convolved layers and (conceptually) convert them into smaller pieces like lines or arcs, then as you have more layers, the liens and arcs convolve into larger images that, in the finally connected layer, will output what the image is.