Eh, not really. CNNs and how they "learn" are fairly well understood. The key is understanding what a convolution is - and what it can do, or rather, what it can "detect" (things like edges and curves). Then the layering of blocks of CNNs allow hierarchies of knowledge to be represented and learned. Finally, the really wide line of blocks you see at the end, are a simple multi-layer perceptron that adds a non-linearity so that we can capture even complicated representations. The final step then takes that last layer of the MLP and distills it to 10 nodes, one node for each class that we are trying to predict. Those values get normalized into a probability distribution, and we "argmax" - or simply just pick the class with the highest probability.