1. The rational way
"Underworld" is another way of saying "subconscious." Basically, what Jung said (and yes, even Freud, as much as I dislike him.) Very little of our consciousness is actually conscious - icebergs, with their 10% visible, 90% submerged are a useful analogy. And speaking of analogies, the subconscious doesn't deal with facts and figures and logic. It's language is myth and poetry and dreams. But the vast subconscious is powerful, and it can either destroy us or gives meaning and beauty to our lives.
Don't get me wrong, I'm not saying that personal growth is the only source of meaning or beauty in our lives. Science is full of amazing, awe inspiring beauty. And there's nothing more meaningful to a mature person than living for something larger than yourself, living for others. But when we've straightened out the knots and blockages in our subconscious, we no longer have violent eruptions of rage or fear hamstringing us and keeping us from living our lives fully. Believe me, I've been there and done that. I spent the last ten years of my life doing activism, and, while I'm proud of it and glad I did it, I know I could have done so much more if I'd been emotionally healthy. But the only way to do that is to work through your emotional issues through your subconscious.
There are many ways to do that; dreams, divination, meditation, etc. All of these are ways to send a line down into the depths of the subconscious, to set up a two way communication. You can figure out why you're doing or feeling what you're doing and feeling, and start releasing the pain and fear that's holding you back. Your subconscious mind will pick out the things and make the interpretations you need to understand consciously to progress to the next stage of your work.
2. The Dreaming Way
The other way to look at this is to take everything at face value: the gods do exist, the tarot and your dreams are speaking to you. Yes YOU. The universe is full of magic, and it's got a message for you if you only open your ears to hear it. This is the way your subconscious self is seeing things, and it's weird the way things seem to work out.
In this way of seeing things, there are two worlds: the "real" world, where the laws of physics works and things have a cause and an effect. And then there's the mythic world, a larger than life world where Platonic archetypes can actively affect your life in the real world.
There's something about human beings that allows these two worlds to meet - there are two sides to our natures that can hook into these two worlds, and we become the place where they join.
Why both ways of seeing are useful
The first way is obvious, but any rational person would ask, why deliberately delude yourself?
The short answer is because it's useful. It works. So long as you don't forget you're dealing with myths and metaphors in order to access your subconscious, its a very powerful tool to straighten out your issues and become a fuller, more whole and healthy human being.
We do have this non-rational side to ourselves. And if it wasn't the source of so much suffering I'd say, fine, let it be. But we often can't release the really bad stuff without going to that part of ourselves, and in order to work with it we have to be non-rational as well. And if it wasn't the source of so much joy I'd say let it be. But it is. When we have these channels cleared and freed from all the garbage, we find we're no longer afraid of others, or of living. We like ourselves. And we like other people. We're hopeful and optimistic, but not blindly so.
This is an important part of ourselves. At least as important as our rational selves, at least to our personal well being. But even to others - how can you possibly help others if you're a complete basket case? How can you even love others or be friends if you're reactive and full of rage, or controlling, or fearful? We can't get stuck mucking about our personal Underworlds - to do so would be self absorbed and, quite honestly, pathetic - but we can't live fully in the "real" world without having done some work there.
The question is: Are we free? Are we living fully, and loving without reservation? If not, then we have some work to do in the Underworld.