The Kuhn-Tucker Theorem is a fundamental result in optimization theory, particularly in constrained optimization problems. It provides necessary conditions for a solution to be optimal when there are constraints on the variables. This theorem extends the Lagrange multiplier method, allowing for inequality constraints in addition to equality constraints. In practical terms, the Kuhn-Tucker conditions help identify optimal solutions in various fields, such as economics and engineering. By analyzing the gradients of the objective function and the constraints, the theorem aids in determining whether a proposed solution is indeed the best possible under the given restrictions.