Tensors
In layman's terms, a tensor is a way of representing the data in deep learning. A tensor can be a 1-dimensional, a 2-dimensional, a 3-dimensional array, etc. A tensor can be a multi-dimensional array. In machine learning and deep learning you have datasets which are high dimensional, in which each dimension represents a different feature of that dataset.
Consider the example of a dog versus cat classification problem, where the dataset you're working with has multiple variety of both cats and dogs images. Now, in order to correctly classify a dog or a cat when given an image, the network has to learn discriminative features like color, face structure, ears, eyes, shape of the tail etc. These features are incorporated by the tensors.