Tensor rank refers to the minimum number of simple tensors needed to express a given tensor. A simple tensor is a tensor that cannot be decomposed further, often represented as the outer product of vectors. For example, a rank-1 tensor can be visualized as a single vector, while higher rank tensors require more vectors to represent their structure. In practical terms, the rank of a tensor provides insight into its complexity and the relationships between its components. Understanding tensor rank is crucial in fields like machine learning, computer vision, and data analysis, where tensors are used to represent multi-dimensional data.