Local invertibility refers to the property of a function where, at any given point within a certain neighborhood, the function behaves like an invertible function, enabling us to solve for input values from output values locally. This concept is crucial in calculus and differential geometry, particularly in the context of the Inverse Function Theorem, which ensures that a differentiable function is locally invertible near any point where its derivative (or Jacobian, in higher dimensions) is non-zero.