When talking about the "strength" of a cigar, we are referring to the power of the tobacco and the amount of nicotine therein. "Strength" does not refer to the amount of flavor, or "body" that a cigar has.
A 'Medium Strength' cigar will have mid-range levels of nicotine and a fair amount of spice to tingle your mouth. As the name implies, cigars in this category will be a nice middle of the road choice. Not too much nicotine, but not so little that you can't feel the cigar.
Medium Cigars are perfect choices for mid day smoking, but are actually quite well blended to be smoked any time, depending on your level of experience. You may want to have had something to eat and some water though, to help tame the nicotine.