So, what makes CNNs "convolutional"? When I hear "convolution", I think of either smearing/blurring together (as in the "convolve" tool in programs like Photoshop), or complexity/tangling (e.g., "a long and unnecessarily convoluted explanation").
The background section in the "On Complex Valued Convolutional Neural Networks" master thesis suggests that CNNs are what has made neural networks actually useful for tasks like computer vision and face recognition. Why remains unclear, however, the term "convolution operation" was mentioned.
Guberman, N. (2016). On Complex Valued Convolutional Neural Networks. arXiv preprint arXiv:1602.09046.