There are myriads ways in which D&D keeps the rules of the game simple in order to facilitate game play quickly and easily. Dungeons & Dragons game mechanics are necessarily an abstraction of the reality they're trying to describe so that they can "keep it simple". D&D rules describe a world that is a mix of the normal, physical reality in which we live and a magical realm of fantasy fiction.
Armor Class (AC) is a reduction of complexity that combines a character's ability to dodge attacks, deflect blows, and absorb hits into a single number. This is an area where D&D has gotten more efficient over time. Current armor class mechanics are much simpler than the THAC0 rules of Advanced Dungeons & Dragons. It doesn't matter whether you're aiming for the head or the heart. You don't have consult a hit location chart to determine whether your character got hit on the hand or the head.
Combat in D&D is faster, simpler, and easier to judge because the core rule consists of a single roll of one die (a 20-sided die or d20) against a static target number (the defending character's AC). You don't have to count the number of dice you get to roll. You don't have to count the number of successes you achieved. You don't have to wait for the defender to roll dice or compare your dice with their results. You don't have to consult a chart to determine the outcome of your attack and the probability that you'll hit a given AC is easy to calculate.
Character classes simplify the complex job of building a person, from a collection of mechanics, down to picking a hero archetype. Once you pick a class you've greatly reduced the number of decisions required to finish your character. D&D has fared better in some of its editions than others when it comes to keeping classes simple enough to meet the K.I.S.S. requirement. Dungeons & Dragons has succeeded because it doesn't use a point-buy character creation system or even the categorized decisions of a game like Vampire: the Masquerade.
I don't want to dismiss complexity. There is a proper place for complexity and amount of it that D&D needs which I'll address in more detail at a later date.