NHibernate's inverse - what does it really mean?

NHibernate's concept of 'inverse' in relationships is probably the most often discussed and misunderstood mapping feature. When I was learning NHibernate, it took me some time to move from "I know where should I put 'inverse' and what then happens" to "I know why do I need 'inverse' here and there at all". Also now, whenever I'm trying to explain inverses to somebody, I find it pretty hard.