Linen stitch, also called Woven stitch, makes a dense, firm fabric with little give or stretch. While it has a tiny bit of drape when done at a reasonable gauge, it can easily become stiff as a board if knit tightly.
This firmness makes it a good choice for home decore type projects like pillow covers or for items needing a stiffer fabric such as tote bags.
My current linen stitch project is a throw for my cats. I hope that the texture of this stitch will allow it to stand up to the occasional kneading from a cat.
Offset rows of alternating knit stitches and stitches slipped with the yarn in front create a mesh of stitches that do more resemble a woven rather than knitted fabric in its characteristics.
The slipped stitches produce a texture that lends itself well to using two or more colors. Knit two rows in each color, starting with a right side row.
Here's the stitch as I'm doing it.
Start with an odd number of stitches.
Row 1 (RS) K1 *slip1wyif, knit1, repeat from *, ending with a K1
Row 2 (WS) Purl
Row 3 K1 *knit1, slip1wyif, repeat from * until two stitches from end, K2.
Row 4 Purl
Note that Row 1 starts and ends with K1 while Row 3 starts and ends with a K2. This offsets the stitches in Row 3 from those in Row 1.