The binary search algorithm employs a divide-and-conquer approach to locate an item within a sorted array or list. It begins by comparing the target value to the middle element of the array. If they are not identical, the algorithm eliminates the half of the array where the target cannot reside and proceeds the search on the remaining half. This process iterates, with each step narrowing down the search range until the target value is discovered. If the search concludes with an empty remaining half, it indicates that the target is not present in the array.