Binary search is a fundamental algorithm that efficiently searches for a target value in a sorted array. The key idea is to divide the search space in half with each step, reducing the time complexity to O(log n). In TypeScript, you can implement binary search using either an iterative or recursive approach. The algorithm begins by comparing the target value with the middle element of the array. If the target matches the middle element, the search is successful. If the target is smaller, the search continues in the lower half of the array, and if it's larger, the search continues in the upper half. This process repeats until the target is found or the search space is exhausted. Binary search is widely used in applications where fast lookups are necessary, such as in databases, search engines, and memory management systems. Mastering binary search in TypeScript is crucial for solving problems where efficient searching is required, especially when dealing with large datasets.