Edges refer to the outer periphery of the petals and occasionally the sepals.
Edges can be structural, i.e. have knobs, braids, tentacles, fringe, and teeth.

This bloom shows knobs, braids, tentacles, and fringe. Cultivar: ‘Magic Lake’. Photo by Patrick Stamile, used with permission.
Edges can also be of a different color. If the edge is narrow and gold, silver, or white, it is referred to as a wire edge.
Edges of a different color or colors can be narrow (referred to as a picotee) or wide (referred to as a border).

Shows a multiple colored border of brown and gold, sometimes called a multiple edge. Cultivar: ‘Sedona’ (Stamile). Photo by Patrick Stamile, used with permission
Some structural edges reach down into the surface of the flower. These super sculpted edges give a three-dimensional quality to the flower.