TensorFlow is a software library for machine learning and deep learning. It uses tensors as multi-dimensional data arrays to represent mathematical expressions in neural networks. TensorFlow is popular due to its extensive documentation, machine learning libraries, and ability to train deep neural networks for tasks like image recognition. Tensors have a rank defining their dimensionality, a shape defining their rows and columns, and a data type. Common tensor operations include addition, subtraction, multiplication, and transposition.