Convolutional Neural Nets are usually abbreviated either CNNs or ConvNets. They are a specific type of neural network that has very particular differences compared to MLPs. Basically, you can think of CNNs as working similarly to the receptive fields of photoreceptors in the human eye. Receptive fields in our eyes are small connected areas on the retina where groups of many photo-receptors stimulate much fewer ganglion cells. Thus, each ganglion cell can be stimulated by a large number of receptors, so that a complex input is condensed into a compressed output before it is further processed in the brain.
If you’re interested in understanding why a CNN will classify the way it does, chapter 5 of Deep Learning with R is a great reference.