A metric tensor is a mathematical object used in geometry and physics to define distances and angles in a given space. It provides a way to measure how far apart two points are and how they relate to each other in terms of curvature. In the context of general relativity, the metric tensor describes the shape of spacetime and how it is influenced by mass and energy. In more technical terms, a metric tensor is a symmetric, bilinear form that takes two vectors and produces a scalar value representing the inner product. This allows for the generalization of concepts like length and angle to curved spaces, making it essential for understanding the geometry of manifolds and the behavior of gravitational fields.