Introduction and Summary
Binary search is a more specialized algorithm than sequential search as it takes advantage of data that has been sorted. The underlying idea of binary search is to divide the sorted data into two halves and to examine the data at the point of the split. Since the data is sorted, we can easily ignore one half or the other depending on where the data we're looking for lies in comparison to the data at the split. This makes for a much more efficient search than linear search.
Binary search is used on sorted arrays, but we see it more often when used with binary search trees (see the trees SparkNote for more information). Whereas linear search allows us to look for data in O(n) time, where n is the number of elements being searched, binary search allows us to do the same search in O(logn) time, a dramatic speed enhancement.
Binary search is one of the most common search algorithms and is useful in most any real world application you might write.