Possible meanings are: because seals were very important, people kept them around their neck or on their hand. The woman wants to be with the man constantly, or a seal shows who owns the thing that has the seal on it, and the woman wants herself as the seal on the man's heart and arm to show that all of his thoughts, emotions, and actions belong to her.
When someone dies, it is as if death does not release the person and let him live again. So also, when someone loves someone, that person does not stop loving the other person.
When someone dies and goes to Sheol, it is as if Sheol does not release the person and let him leave. So also, when someone is jealous, he does not stop being jealous for that person.