The Viterbi algorithm is a dynamic programming technique used to find the most likely sequence of hidden states in a hidden Markov model (HMM). It efficiently computes the best path through a set of states based on observed data, making it useful in various applications like speech recognition, bioinformatics, and error correction in digital communications. By breaking down the problem into smaller, manageable parts, the Viterbi algorithm reduces computational complexity. It uses a recursive approach to evaluate possible state transitions and keeps track of the highest probability paths, ultimately providing the optimal sequence of states that best explains the observed events.