Good question! Let's attempt to answer by giving an example. Deanie Etcetera is greatly in love with Mitch Longley, the actor. She wrote him fan mail, being honest with him about her feelings towards him. Eventually, Mitch Longley told Deanie that alas, he wasn't interested. He hoped that she could "respect that". This means that Deanie could/would respect Mitch Longley's decision and accept the sad fact that Longley was not interested in becoming romantic with her.
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The phrase "I can respect that" means ... pretty much what it says. The person saying it may not agree with what you have just said, but they understand it and accept the decision.