A tangent bundle is a mathematical structure that combines all the tangent spaces of a differentiable manifold into a single entity. Each point on the manifold has an associated tangent space, which consists of all possible directions in which one can move from that point. The tangent bundle collects these spaces, allowing for a comprehensive study of the manifold's geometry and calculus. In more technical terms, the tangent bundle is a new manifold formed by taking the product of the original manifold with its tangent spaces. This construction is essential in fields like differential geometry and theoretical physics, as it provides a framework for analyzing curves, surfaces, and other geometric objects.