Most of the recent advances in AI depend on deep learning, which is the use of backpropagation to train neural nets with multiple layers ("deep" neural nets).
Neural nets consist of layers of nodes, with edges from each node to the nodes in the next layer. The first and last layers are input and output. The output layer might only have two nodes, representing true or false. Each node holds a value representing how excited it is. Each edge has a value representing strength of connection, which determines how much of the excitement passes through.
The edges in an untrained neural net start with random values. The training data consists of a series of samples that are already labeled. If the output is wrong, the edges are adjusted according to how much they contributed to the error. It's called backpropagation because it starts with the output nodes and works toward the input nodes.
Deep neural nets can be effective, but only for single specific tasks. And they need huge sets of training data. They can also be tricked rather easily. Worse, someone who has access to the net can discover ways of adding noise to images that will make the net "see" things that obviously aren't there.