A neural network mimics human brain functions by utilizing layers of interconnected nodes, or neurons, that process and transmit information. Each neuron receives inputs, applies a mathematical function, and passes the results to the next layer in the network. This architecture enables the system to learn patterns through training on vast datasets, adjusting the connections based on the input-output relationships observed. Neural networks excel in tasks like image recognition, natural language processing, and decision-making, showcasing their ability to approximate complex functions similar to human cognitive processes.