Neural network
Also called: neural net
In one sentence
A large stack of simple mathematical operations whose adjustable values are tuned during training.
In more depth
Loosely inspired by biological neurons, but not a model of the brain. Inputs are multiplied by weights, summed, and passed through a function that determines how much signal continues.
The capability comes from scale and training, not from any single component. A modern network has billions of weights, all set by the training process rather than by hand.