Algorithm complexity refers to the computational resources required to execute an algorithm, typically measured in terms of time and space. It helps in understanding how the performance of an algorithm scales with the size of the input data, allowing developers to choose the most efficient algorithm for their needs. There are two main types of complexity: Time Complexity, which measures how the execution time of an algorithm increases with input size, and Space Complexity, which assesses the amount of memory an algorithm uses. Understanding these complexities is crucial for optimizing algorithms and ensuring efficient program performance.