The bar increase is called a bar incease because it creates a purl bar
The bar increase is called a bar incease because it creates a purl bar on the knitting. To make a bar increase simply knit in the front and back of the same stitch. As you knit the stitch, you create a regular knit stitch. When you knit in the back of the stitch, you create the purl bar.
This increase has limitations. On a stockinette stitch fabric, it is usually highly visible. Exceptions would be in dark fabrics and very fuzzy fabrics. It can also be used in unseen areas like under the arm.
One great use is in ribbing. Many patterns require one or several increases on the last row of the ribbing. Work the increase on a knit stitch, this will maintain the column of knit stitches in the ribbing. When you knit in the back loop and create a purl bar, it tucks itself into the purl channnel and goes unnoticed.