There are two meanings of the term "broaching stitch".
First meaning of this term symbolizes small part of yarn, which is located between two neighbouring sts. You can see it better if your work is located on two knitting needles. The broaching is located between edging sts, one of which is located on the left-hand needle, and another one on the right-hand needle. When the descriptions of work says, that you need to add one broaching chain, catch this part of work with right-hand needle and make new st with its help, extending the working yarn inside the ball.
Second meaning greatly differs from the first. If by means of the previous broaching the quantity of sts increases, but making the second way of broaching you can decrease the quantity of sts. This method is used in several different situations while knitting. It's best seen while binding off the sts of the last row of work in classic way. In this case, everything depends on the quantity of sts, which you need to decrease. If it's just one st, so you just need to place it from left-hand to right-hand needle. When you need to decrease more sts, so you need to transfer them in the needed quantity. Transfer of sts is made without knitting them. Then, knit the next knit st or purl, depending on the ornament. Draw the last knitting st through the slipped st or chains. Using this method, you can decrease the needed quantity of sts.
Wide-spread technique of decreasing sts is forming the arm-holes or reglan sleeve. This method is made from the right-side of your work. You can make decline either to left, or right side. In order to make left declain you should slip the first st. Then, make knit st and draw it through the first slipped st. Decreasing the quantity of sts with right declain, start knitting with the first knit st. Then, slip the second st and place both sts on the left-hand needle. Draw the first st through the second and leave it on the right-hand needle.