Before I discuss the uses of this increase, let me illustrate how it is done.
Make 1 left (backward loop): M1L (bl)
Make 1 right (backward loop): M1R(bl)
You can see that I employ EZ's suggestion, which she illustrates in her video, "Knitting Glossary", to wrap the left-leaning increase around my first finger and the right-leaning increase around my thumb. Don't get caught up in the mechanics of winding the wool. Focus on the direction of the crossed over yarn and make it happen by whatever means works for you. ALWAYS WORK INTO THE BACK OF THE M1R(BL) ON THE NEXT ROW. Otherwise, the whole thing will unwind itself.
When I first read about this method, I thought, "What? That's going to leave a great gaping hole!" It's true that this increase is in some circumstances more visible than the type of M1 that is worked into the horizontal strand between two stitches. But, there are situations where, believe it or not, this increase is the most invisible.
1. In garter stitch, you can work paired increases almost invisibly with the backward loop increase. I used this method in the lower body of my just-completed Harriet jacket (not yet published).
The problem with the more commonly used M1 is that when you work into the horizontal strand between 2 stitches, you disrupt the flow of the garter stitch ridges. The lines become distorted. Knitting into the front and back of the stitch (kfb) is a better choice in general for garter stitch, but in cases where you want the cloak of invisibility, the backward loop method is best. See?
This is the side of the peplum-like lower portion of Harriet. There are paired increases going on here, but it's really hard to pick them out.
2. If you are working with a woollen-spun yarn, such as Peace Fleece, or BT's Shelter, you can use the backward loop method for increasing in a sleeve worked in the round. The fuzzier nature of woollen-spun yarn helps the increases to blend in, and the backward loops are simple to work. Remember, EZ's knitting was all about simplicity.
3. I like to use the backward loop method when increasing for insets as in Brookline. Because this type of increase does not create any tension on neighbouring stitches, it allows for a smooth, uninterrupted line along the edge of the inset.
This is a view of the WRONG ISIDE of the gores in Brookline. Because it is less well known, the Twist Collective editors decided not to include the backward loop increase, so when you read the published version of this pattern you will notice that there is no reference to it. Nevertheless, if you're knitting Brookline, give it a try. You'll like it.