What does it mean to crochet around a stitch?

My best guess to what you are asking is that you are referring to Front Post and Back Post stitches.

This would mean that you sitch around the stitch below the one that you are making. Either by bringing your hook in from the "front" (Front Post) or the "back" (Back Post).

The added Links would be good to view to see what is meant by "Front Post" and Back Post.