Note: this explanation refers to the term tensor as typically used in popular machine learning libraries like TensorFlow and PyTorch. The mathematical definition is slightly different.
A multidimensional array similar to numpy.array.
Tensor is a term that is used in TensorFlow and PyTorch to indicate a multidimensional array. This may be a bit confusing because the mathematical term tensor has a different meaning. The math tensor is a function, that can be represented as an array.
Tensors are data structures that store data. For example, a 1D tensor could store prices of houses, a 2D tensor could store an image, a 3D tensor could store multiple images, etc.