Binary search is a highly efficient algorithm used to search through a sorted array in O(log n) time by repeatedly dividing the search interval in half. To implement this in TypeScript, you start by defining two pointers: `low` and `high`, which represent the bounds of your search space. At each step, you calculate the middle index, compare the middle element with the target value, and adjust the pointers accordingly. If the target is less than the middle element, you search the left half of the array by updating the `high` pointer. If the target is greater, you search the right half by adjusting the `low` pointer. Binary search is ideal for scenarios where you need quick lookups in large sorted datasets, like searching for a value in a sorted array of numbers or strings. The TypeScript implementation involves writing a function that takes a sorted array and a target value as inputs and returns the index of the target if found or `-1` if the target is not in the array. Binary search is an important concept to master, especially when working with algorithms that require fast search capabilities, such as in search engines or databases.