In short: By using Attacks of Opportunity in your old school or OSR D&D game, you can up the ante in combats – just remember to keep it simple.
Attacks of Opportunity (or Opportunity Attacks in the more modern parlance) is a rule that was introduced in D&D 3.0, and has been part of Dungeons & Dragons ever since.
Older versions of the game – like Old School Essentials (OSE) and B/X – never had a rule that covered this as it was left completely up to the GM, never even considered, or handled in a different way (long weapons going first in melee combat, is an example in AD&D).