Power refers to how much larger an object is made to look through a magnifying lens. Unfortunately, there are two different conventions for computing power that lead to different results. Below is an example of how two power ratings can be achieved for the same 8 diopter lens. Formula A says that the 8-diopter lens makes an object look 2 times bigger, over and above what the unaided eye already sees. Formula B says that the 8-diopter lens makes an object appear 3 times larger than it actually is.
Focal length is important when the task requires using tools with the object being viewed.
Because focal length decreases as power increases, there is less room to perform work on an object under higher power lenses. The field of view is the size of the magnified area under the lens that is in focus. The field of view decreases as power increases. More powerful lenses make small details look big, but less of the total object is visible. Proper lighting is equally important as magnification in achieving a good viewing situation.