A popcorn stitch is used to create extra texture in anything you are knitting. It can be used either in garter stitch (straight knitting rows), or stockinette stitch (knit one row, purl one row). It forms little "knots" throughout the knitted item.
The popcorn stitch is made by knitting and purling in the same stitch (increasing in that row), then slipping the new stitches over a stitch on the next row (decreasing back in that row).
For example, if you were creating a popcorn stitch with five stitches, in the first row you would knit 1, purl 1, knit 1, purl 1, knit 1; in the next row, you would slip those first four stitches, knit 1, then slip each of those four stitches over the knitted one. You can adjust the size of the popcorn or "knot" you want by how many times you knit and purl in one stitch. Usually four or five times is plenty. More than that and it becomes too difficult, especially if you are working with thick yarn.
If you are knitting a garment such as a sweater, the key to any textured knitting stitch is to be careful which side of the item you are knitting on; be sure you put all of the stitches that stand out on the same side. If you mark the right side of the fabric, you will always know when and where to start your popcorn stitch. This is extremely important when working in garter stitch, where you are knitting every row and both sides look the same. If you are knitting a scarf or an afghan, you may want the texture to show on both sides.
The popcorn stitch can be used instead of the ribbed stitch (knit 1 stitch, purl 1 stitch across the same row) as a decorative trim around a sweater bottom, or around sleeves. It is used quite often in afghans. It can also be used for brims on hats and around the wrists of mittens. You can use a popcorn stitch to create a raised form in any knitted article (such as a flower). Sometimes, a popcorn stitch is even used for buttons to create a hook-and-loop enclosure. Wherever the knitter wants texture in an item or would like to break up a boring pattern, the popcorn stitch will add flair.