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A convolutional neural network is a type of neural network aimed at image processing, generally image recognition. This general strategy regarding image-handling is inspired by processing of images within the brain and is currently a successful strategy in developing similar skills in software.
A neural network is a type of artificial intelligence (AI) program modeled after the apparent microstructure of brain matter: a network consisting of links transferring data between nodes (termed neurons, both in the brain and in such software), the nodes processing/combining the data and passing it on through other such links to other nodes.
These neurons may perform logical operations based upon data received through multiple links, or may respond to the amounts or ratios regarding such received data, the neurons all implemented by a single program along with data specific to the individual neuron regarding what operations it will perform. Decisions are made through based upon data entered into some neurons taking input, and passing them along, each neuron performing its operation, eventually providing the output. Generally, the neuron program is designed so the it can adjust its defining data through feedback: an indication of the success of the network's entire operation. In the case of image recognition, this would be telling the network after the fact whether the answer produced was correct, e.g., for a network to recognize cars, an indication of "this is indeed a car" or "this is not". Typically, the neural network has a mode for accepting such feedback (termed training or learning), so example data can be fed into it, along with the correct answers, giving the network the opportunity to adjust its neurons, basically to program itself. After such training, the network can be tested to see how well it performs. Given sufficient computational capacity to implement large, fast networks, this has been a very successful AI strategy, but has the disadvantage that it can be very difficult to understand how a resulting large network makes its decisions, and there have been cases where decisions were actually based upon something accidently consistent during the training, leading eventually to odd and dramatic malfunctions.