Continuity Editing: This is when one shot moves onto another will a smooth clean change, that is very unrecognisable to the audience, and doesn't create disorientation. One example of filming that does not do this is Discontinued filming, used in foreign films mostly, and shows the change of shot very clearly, causing somewhat confused to the narrative.
It includes two different categories of cutting; one is Temporal cutting, which connects shots together to support the narrative development. It may be linear progression or not, and can include flashbacks and flash forwards, these are both used to establish the progression of time.
The other category is Spatial cutting, which creates unified space through editing the shots from different angles and framing. This includes things such as shot/reverse shot, the Kuleshov effect, and parallel editing.
Spatial Editing: This is the act of placing the shot of one location, with a shot from another, and using them to construct film narrative in any imaginable way.
Within this form of editing, there is the 180 degree rule, which states that, in the 360 degree radius of the set, when filming direction interaction between 2 characters, that all cameras and camera movement mist be on one side of the set only, covering '180 degrees'. Within this side of the set, there is two cameras, one behind each character that will film the opposite characters reactions, and can be edited to make a short interaction/conversation. This is done to prevent disorientation of the audience, and make the scene look natural. Another form of editing that is used in Spatial editing is the shot/reverse shot, which is a little similar to the 180 degree rule, as two cameras are placed behind each characters that are having a conversation, and the whole conversation is filmed over the shoulder, but is kept stationary.
The last form of editing that is used in Spatial editing is the Match on Action shot, which is when an action shot is filmed, possibly a character reading a book. And the shot is cut half way through the action, and another filmed shot is placed directly after this cut, showing the certain action carried on, but in a different shot, often zoomed in.
I think that continuity editing is important when filming because it is essential that the transition between shots is as smooth as possible to ensure that the audience has maximum enjoyment form the film and that no attention is drawn to the change in shot.