For example if I give an LLM without user seperation this text:
"It's a lovely day." It might continue with "The sun was shining."
But with user separation it focuses on responses to "it was a lovely day" from other users and the training data might suggest "I agree, it's wonderful weather."
So interaction with an LLM is like posting on a forum, it gives you and average of typical responses with one small change: most LLMs have a strong positivity bias programmed in.