The Metric Tensor in General Relativity is a Set of 10 parameters ascribed to each point in space, the values of which describe the geometry of spacetime.
Metric means “measure,” and a tensor is simply the higher dimensional analogue of vector, i.e. it is a 3-dimensional vector. A tensor can usefully be visualized as a field of vectors.
The values of the ten parameters at each point in space are displayed in a Matrix, an array of numbers which together provide a description of the current parameters and rate of change of those parameters at that point in space.
The Metric Tensor in General Relativity is denoted 