The Snail Trail Stitch is a linear stitch that looks like a string of fish or little ribbons to me. When you use it around a flower dot, the flower looks as if it's winding up for take off like these above. (Where the reference to snails came from is lost on me. Any ideas?)
Here's how I make my Snail Trail Stitches: bring the needle and thread up at point A. Insert the needle at point B which is about 1/8" to the right and 1/8" up from A. Bring the needle under the fabric and exit at a point about 1/4" up from A at point C. Slip the thread over the needle and then snugly under the needle. Now pull the needle and thread gently through point C. Don't pull too tightly or you loose your loop.
What was point C now becomes point A. Repeat the above directions to form a loopy line across the fabric. I noticed that this stitch requires a lot of the right hand working with the left hand. (You'll be happy to know that so far they are getting along.) This stitch also reminds me of a song from my youth by Dale Evans. Maybe you remember it. "Happy Snail Trails to you, until we meet again. Happy Snail Trails to you, keep smilin' until then!"