Through the Back Loop

To knit or purl through the back loop you must first understand that stitches in the ready-to-work position have a front and a back.
The front of the stitch is the loop closest to you, is the part of the loop on your side of the needle.
The back of the stitch is the loop farthest from you,is the part of the loop on the side the needle facing away from you.

In regular knitting you form the knit stitch by putting your needle (from left to right) through the front loop on the left hand needle.
1. To knit, insert the right hand needle from left to right through the front of the first stitch on the left hand needle

To knit through the back loop, you’re changing the direction from which the needle enters the stitch and deliberately twist the stitch and create a different effect. This technique is sometimes used to create textured stitch patterns, as well as some twisted rib effect.

2. To knit into the back of a stitch, Insert the needle into the back of the stitch on the left hand needle .

To purl through the back of the loop: Insert your needle through the back of the loop from right to left and purl as normal.

Twisting stitches as you work them gives extra neatness and firmness to finished patterns.
1. Stockinette Stitch
2. Crossed Stockinette Stitch: Pattern can be worked on any number of sts. 1st row: knit all stits through the back loop. 2nd row: purl all sts.