The algorithm widely used for sorting and searching data is known as the quicksort algorithm. Quicksort is favored for its efficiency and effectiveness in handling large datasets, particularly due to its average-case time complexity of O(n log n). It operates using a divide-and-conquer approach, selecting a pivot element and partitioning the data into smaller segments. Its straightforward implementation and adaptability for various data types make it a popular choice among programmers for sorting tasks in a variety of applications.