Focus stacking is an image processing technique that involves the merging of photos taken at different focal lengths into one final photo with better Depth of Field. A great example would be a photo involving two mating insects or spiders etc., most of the time you will not be able to take a shot with both male and female in focus at high magnification, regardless of the angle you use (see photo below).

Fleshflies Humping Action! This single shot was taken WITHOUT focus stacking. If you enlarge the photo, you will notice that the male fly at the back is actually Out-of-Focus (OOF) due to the shallow Depth of Field when taking highly magnified shots.

I took this photo using iphone 5s plus macro lens