In the absence of anything to the contrary, the edge of a charge or ordinary, or a division of a field, is an appropriately straight or curved line. However, not all charges are edged that way.
A charge is said to be indented if its edge is made of even zig-zag lines. In normal circumstances, points on opposite sides face away from each other: if the peaks on one side match troughs on the other (so, for example, in the case of a fess making a broad zig-zag line) then the term is dancetty.
|The arms of Berry|
An edge that looks like a set of battlements is embattled - a square wave, if you like. If the battlements have multiple steps, it's battled embattled or embattled grady. If the upward edges go past the vertical, the term (which is obvious once you look at it) is dovetailed.
If we move from a 'square wave' edge to a sine wave, the term is wavy. If the waves go past the vertical (like dovetailed) the analogous term is nebuly. An edge that looks like breaking waves is wavy crested.
The other common line type is a series of circular arcs joined at their points (like the edge of a cookie cutter). If the points are outward, it's engrailed, inward, it's invected.
Once again, we've well exceeded the limit of what the free version of Coat of Arms Design Studio can handle, so I'm ducking out of drawing too many diagrams. There are a beautiful set of examples on the Wikipedia page, as well as a whole load of more obscure terms.
Note above, the arms of Berry: azure, three fleurs-de-lys or, a bordure engrailed gules. In this case, the bordure or border is a mark of cadency, as the dukedom was (rather like the Duchy of York in England) given to younger sons of the French king (azure, three fleurs-de-lys or being France).