This configuration allows bigger apertures without longer tubes :bigger aperture ==> more light assimilated ==> fainter objects are better viewed.
Since they depend on parabolic mirror to concentrate the light, they don't suffer from chromatic aberration.
The same magnification formulas as refractors apply. But since they give less sharp images then refractors, try to avoid getting too close to the maximal magnification allowed.
They have an inconvenient : the mirror focus can get displaced while moving the telescope, so collimation needs to be adjusted sometimes, or else you get an image with a trailer.
Refractors are great for faint objects, such as nebulae, specially when using a large aperture with lesser magnification.
They are also good for planets, such as Jupiter and Saturn taken with our 4,5" reflector :
