What Backtracking Solves
Backtracking is a general technique for exploring a combinatorial search space by incrementally building candidate solutions and abandoning partial states that cannot lead to a valid final answer.
Conceptually, backtracking performs a depth-first exploration of a search tree where each node represents a partial solution, each edge represents a choice, and failed branches are undone so the algorithm can try another possibility.
Reference:
the presentation follows the classical treatment used in
algorithm design and combinatorial search,
connecting recursive exploration, pruning, and search trees.