The Halting Problem is a fundamental concept in computer science that addresses whether a computer program will eventually stop running or continue indefinitely. Proposed by mathematician Alan Turing in 1936, it demonstrates that there is no general algorithm that can determine the halting behavior of all possible programs for all possible inputs. In essence, the Halting Problem shows the limitations of computation. If we could create such an algorithm, it would lead to contradictions, as it could be used to construct programs that behave unpredictably. This result has profound implications for the fields of theoretical computer science and mathematics.