It is a straightforward recursive, nondeterministic, depth-first, backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the dancing links technique.
[1][2] The exact cover problem is represented in Algorithm X by an incidence matrix A consisting of 0s and 1s.
Knuth's main purpose in describing Algorithm X was to demonstrate the utility of dancing links.
Because exact cover problems tend to be sparse, this representation is usually much more efficient in both size and processing time required.
DLX then uses dancing links to quickly select permutations of rows as possible solutions and to efficiently backtrack (undo) mistaken guesses.