TensorFlow, as the name shows, is a framework to define and run computations including tensors. A tensor is a generalization of vectors and matrices to potentially higher dimensions. TensorFlow represents tensors as n-dimensional arrays of base datatypes.
When writing a TensorFlow program, the main object you manipulate and pass around is the tf.Tensor. A tf.Tensor object represents a partially defined computation that will eventually produce a value.
An operation allocates memory for its outputs, which are available on endpoints :0, :1, etc, and you can think of each of these endpoints as a Tensor.