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 optimal path through a set of states based on observed data, making it valuable in various applications like speech recognition and bioinformatics. By breaking down the problem into smaller, manageable parts, the Viterbi algorithm evaluates possible state sequences and selects the one with the highest probability. This approach reduces computational complexity, allowing for faster processing of sequences, which is essential in real-time systems and large datasets.