Final answer:
The purpose of listening that involves understanding a message and remembering important information is Comprehensive listening. It requires active engagement and retention of critical elements, distinguishing it from discriminative, appreciative, and critical listening.
Step-by-step explanation:
Of the four purposes for listening, the one that requires people to listen to understand a message and remember important information is Comprehensive listening. This type of listening entails being fully engaged with the communication process, focusing on comprehending the speaker's message, and retaining the critical elements for later recall. It is distinguishable from discriminative listening, which involves distinguishing between different sounds and verbal nuances; from appreciative listening, which is about enjoying the listening experience; and from critical listening, which is about analyzing and evaluating the content of the message.
Comprehensive listening is akin to proactive reading strategies, where you aim to understand what you read, look up unknown words, take meaningful notes, and ask questions to grasp complex texts better. Similarly, when practicing comprehensive listening, one should pay attention to the ideas expressed, question parts that are not understood, make predictions on the message's direction, and seek clarification to ensure understanding.