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.
Full strength cigars are not for the novice or faint of heart. The level of nicotine and spice in this level is high. You will know when you are smoking a full strength cigar, because you will be able to feel the nicotine affecting you, and it can make you feel sick if you are not prepared.
Full strength cigars are best smoked after a heavy meal, for two reasons. First, the food in your belly will help to counteract the nicotine hit. Second, after a full meal, you need a fuller cigar that can get in front of all those heavy flavors from that food.