Merge sort is a popular sorting algorithm that works by dividing an array into two halves, sorting each half, and then merging the two halves back together in sorted order. It is a divide-and-conquer algorithm, which means that it breaks the problem down into smaller subproblems and solves them recursively.
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Here's how the merge sort algorithm works:

1. Divide the array into two halves.
2. Sort the left half recursively using merge sort.
3. Sort the right half recursively using merge sort.
4. Merge the two sorted halves back together.
To merge the two sorted halves back together, we use two pointers to keep track of our progress through each half of the array. We compare the elements at the current position of each pointer, and add the smaller of the two to our output array. We then increment the pointer of the array that we took the smaller element from, and continue until we have merged all of the elements from both halves into a single sorted array.

Here's an implementation of merge sort in Rust:
``` 
fn merge_sort(arr: &mut [i32]) {
    if arr.len() > 1 {
        let mid = arr.len() / 2;
        let (left, right) = arr.split_at_mut(mid);

        merge_sort(left);
        merge_sort(right);

        let mut i = 0;
        let mut j = 0;
        let mut k = 0;

        while i < left.len() && j < right.len() {
            if left[i] < right[j] {
                arr[k] = left[i];
                i += 1;
            } else {
                arr[k] = right[j];
                j += 1;
            }
            k += 1;
        }

        while i < left.len() {
            arr[k] = left[i];
            i += 1;
            k += 1;
        }

        while j < right.len() {
            arr[k] = right[j];
            j += 1;
            k += 1;
        }
    }
}
``` 

Now, as for the benefits of merge sort over bubble sort, there are several:

1. Merge sort has a time complexity of O(n log n), which is much faster than the O(n^2) time complexity of bubble sort. This makes merge sort a much better choice for sorting large arrays.
2. Merge sort is a stable sort, which means that it maintains the relative order of equal elements in the array. Bubble sort is also stable, but some other sorting algorithms are not.
3. Merge sort is a divide-and-conquer algorithm, which makes it easier to parallelize. This means that merge sort can take advantage of multiple processor cores or even multiple machines to sort an array more quickly. Bubble sort, on the other hand, is not as easily parallelizable.
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