The A* algorithm works by searching through a graph or grid to find the shortest path between two points. It starts at the initial node and expands its search by considering neighboring nodes, prioritizing those with the lowest estimated cost to reach the goal. The cost is calculated using a heuristic function, which estimates the remaining distance to the goal. The algorithm continues to explore nodes until it reaches the goal or exhausts all possible paths. By combining the strengths of Dijkstra's algorithm and the Greedy Best-First-Search algorithm, the A* algorithm achieves an optimal balance between speed and accuracy.