Magnification

Magnification is one of the basic scope characteristics.  It measures how many times better you can see an object than with your naked eye.  Some rifle scopes offer a range of magnification, for instance anywhere from 3x to 9x.

Field of View
    
Field of View is the actual width of your scope's sight picture at a specific distance. For example, at a range of 200 yards, a scope can give you a sight picture that is 20 feet wide.

Field-of-view is a function of both magnification and the focal lengths of the lenses. A key point to keep in mind is that the higher your magnification is, the narrower the field of view is.

Stray Light

When light enters the scope and reflects off of the metal, it reduces the image quality of the target.  This is why you want to find a scope that has interior coating, to prevent reflection off of the metal,.

Eye Relief
   
Eye relief is simply the distance between your shooting eye and your eyepiece lens. If your eye relief is too small, there is a risk of hitting your eye with the eyepiece when your rifle recoils. 

A general rule of thumb is:  higher magnification and field-of-view equals shorter eye relief.

Exit Pupil
    
This is a measure of the amount of light that reaches your shooting eye.

Length
    
Length is straightforward.  It measures your riflescope, from the leading edge of the objective lens to the back edge of the eyepiece.  Longer models tend to have greater magnification.  However, some shooters prefer shorter scopes for their weight and smaller profiles. 

Center Tube Diameter
    
Your scope's center tube diameter affects its durability.  It also determines what size rings and base you need for mounting, as well.