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 'Mild Strength' cigar will have low nicotine levels and less of that tingling spice hit, therefore making for a more mellow smoking experience. Most of your light, Connecticut wrappers will be in this category and these mild cigars are perfect as a morning cigar. When your palette is clean and able to pick up the nuances of such a mild tobacco. The morning is also when you want less of a nicotine hit.
A mild cigar is a good place to start when you are just getting into cigars too. They make a nice starting point to gauge what you will like.