Binary Search Algorithm in JavaScript is a fast and efficient search algorithm that works by repeatedly dividing the input data in half until the desired element is found or it is determined that the element does not exist in the data. The algorithm starts by comparing the middle element of the data with the target element. If the middle element is equal to the target element, the algorithm returns the index of the middle element. If the target element is less than the middle element, the search continues in the left half of the data. If the target element is greater than the middle element, the search continues in the right half of the data. This process repeats until the target element is found or it is determined that the element does not exist in the data.

To implement binary search in JavaScript, you can write a function that takes in two arguments: an array of elements and a target element to search for. The function should use a while loop to repeatedly divide the input data in half until the desired element is found or it is determined that the element does not exist in the data. The function should return the index of the target element if it is found, or -1 if it is not found.

Here is an example of a binary search function in JavaScript:

```function binarySearch(array, target) {
let start = 0;
let end = array.length - 1;

while (start <= end) {
let mid = Math.floor((start + end) / 2);
if (array[mid] === target) {
return mid;
} else if (array[mid] < target) {
start = mid + 1;
} else {
end = mid - 1;
}
}
return -1;
}
```

This function takes an array and a target element as arguments and returns the index of the target element if it is found in the array, or -1 if it is not found. The function uses a while loop to repeatedly divide the input data in half until the desired element is found or it is determined that the element does not exist in the data.

Note: The binary search algorithm works only on sorted arrays. So, it’s recommended to sort the array before using the binary search algorithm.

Here is an example of how you can use the binary search function:

```let array = [1, 2, 3, 4, 5, 6, 7, 8, 9];
let target = 5;
let result = binarySearch(array, target);
console.log(result); // Output: 4
```

In this example, we first define an `array` of elements to be searched, which is `[1, 2, 3, 4, 5, 6, 7, 8, 9]`. We then define the `target` element we want to search for, which is `5`. Finally, we call the `binarySearch` function, passing the `array` and `target` as arguments, and store the result in a variable called `result`. We then log the result to the console, which should be `4` since `5` is the fifth element in the array and the first index in JavaScript arrays is `0`.

Let’s take a closer look at the binary search function and see what each section of the code does:

```function binarySearch(array, target) {
let start = 0;
let end = array.length - 1;
...
}
```

This is the declaration of the `binarySearch` function, which takes two arguments: `array` and `target`. The `start` variable is used to keep track of the start index of the current portion of the array that is being searched, while the `end` variable is used to keep track of the end index. Both `start` and `end` are initialized to `0` and `array.length - 1` respectively, which corresponds to the first and last indices of the array.

```while (start <= end) {
...
}
```

This is the start of a `while` loop, which will run until the `start` index becomes greater than the `end` index. This means that the target element has been found, or it has been determined that it does not exist in the array.

```let mid = Math.floor((start + end) / 2);
```

This line calculates the middle index of the current portion of the array that is being searched. The `mid` variable is calculated by adding the `start` and `end` indices and dividing the result by `2`. We use `Math.floor()` to round down to the nearest whole number, since array indices must be integers.

```if (array[mid] === target) {
return mid;
} else if (array[mid] < target) {
start = mid + 1;
} else {
end = mid - 1;
}
```

In this section, we first check if the middle element of the current portion of the array is equal to the target element. If it is, we return the `mid` index, which is the index of the target element in the array. If the middle element is less than the target element, we set the `start` index to `mid + 1`. This narrows the search to the right half of the array, since we know that the target element cannot be in the left half. If the middle element is greater than the target element, we set the `end` index to `mid - 1`. This narrows the search to the left half of the array.

```return -1;
```

Finally, after the `while` loop has finished, we return `-1` to indicate that the target element was not found in the array. If the target element was found, the function would have already returned its index before reaching this point.

The binary search algorithm is a popular and efficient method for finding an element in a sorted array. It is a type of search algorithm that divides the array into halves and repeats the process until the target element is found or it can be determined that it does not exist in the array.

Aside from binary search, there are other search algorithms such as linear search, jump search, and ternary search. The most effective search algorithm depends on the size of the array and the nature of the data. For smaller arrays or unsorted data, linear search may be the best choice. For large arrays with sorted data, binary search is usually the most efficient option.

In general, when searching for an element in a sorted array, binary search is the preferred algorithm due to its average time complexity of O(log n), which makes it much faster than linear search for large arrays. On the other hand, if the array is not sorted, or if you need to search for multiple elements, linear search may be the better option.

In conclusion, it is important to understand the trade-offs between different search algorithms and choose the one that is most suitable for your specific use case. Whether you are working with a small or large array, or sorting data or not, the right search algorithm can make all the difference in terms of efficiency and performance.