Tensors are effectively Multi-dimensional arrays that enable you to perform complex operations on multi-dimensional arrays. However, they are not just an N-dimensional array. A Tensor also includes the transformations such as dot product, addition, matrix multiplication, etc.
But why are they important?
Tensors are not new. They have been in use for since long, but their characteristics are heavily exploited in the area of Deep Learning, where the data is usually huge and of multiple dimensions.
Tensors, just like Numpy arrays, also have a shape and data type. But what makes them different from usual Numpy arrays is their ability to utilize GPU memory and compute power which is of utmost importance when data is high-dimensional and size is in millions or more.
Tensors are highly used in Deep Learning frameworks such as Facebook’s Pytorch and Google’s TensorFlow, which is even named after them! 
Google has also developed another AI accelerator, called Tensor Processing Unit (TPU), especially for TensorFlow which takes the optimization to a next level altogether!