A player has perfect recall when the information sets never erase that player's previously available information or earlier chosen actions. With perfect recall, randomizing once over complete pure strategies and using suitable independent randomizations at information sets can induce the same outcome distributions.
Without perfect recall, one information set may be encountered twice on the same play path. A behavioural strategy then uses the same probabilities with fresh draws at both encounters; its outcome distribution need not be attainable by any mixed strategy over deterministic plans.
New to topics? Read the docs here!