Duh, I guess I could look at the pattern myself - you linked it, after all
The slipping of the stitches is just to make a nice edge on the scarf. A lot of times people will slip the first stitch and knit the last stitch of every row to make a nice edge. This is just another way to do it, I guess. You slip knitwise the first and last stitch of every right side row, and looks like you purl the first and last stitch of every wrong side row.