Good news: a literary agent asked to see my manuscript. I obliged her because I am considerate like that.
You don't need a literary agent if you plan to self-publish. All you need is money and a rudimentary grasp of the written language, and honestly some people treat that second requirement as more of a suggestion.
You can usually skip the agent if you plan to publish with a small or academic press, particularly if your book is nonfiction. Even some of the medium-to-largish presses will accept un-agented manuscripts, though looking through the slush pile is usually a low priority. It could be months before they get around to reading it.
If you have written the best novel in the history of Western civilization--Crime and Punishment (but more thoughtful) mixed with Jane Eyre (but more romantic) mixed with Hitchhiker's Guide to the Galaxy (but funnier)--you will die in obscurity, impoverished and alone, or at any rate you won't get published by the Big Five.
Literary agents are flooded with requests to look at people's writing. These requests usually take the form of a query letter, which usually consists of a short pitch, a synopsis or outline, and a short sample of the manuscript.
If the agent is persuaded by the query, she will ask to see the full manuscript. (This is the stage I'm at.) If she thinks she can sell it, she'll agree to represent the writer, thought she'll probably suggest manuscript revisions before she's willing to shop it around. Only after all these hurdles have been cleared will the agent consider sending the book to the big boys: Hachette, HarperCollins, Macmillan, Penguin Random House, and Simon & Schuster.
In other words, it's extremely difficult to get your manuscript into the hands of a Big Five publisher, to say nothing of selling it. The odds of achieving publication are infinitesimal.
But it sounds more fun than other long-odds activities, like climbing trees in thunderstorms to see if you can get stuck by lightning.
I don't want to self-publish. I'm no Dostoevsky or Brontë, not even one of the lesser ones, but I'm not horrible. That's not enough to stand out in the self-pub crowd, unfortunately. Everybody and her brother (the one with the rudimentary writing skills from the second paragraph; remember him?) has self-published. My book, although not-horrible, would barely stand a chance of being found online. Nor would it be found in bookstores or libraries, which typical don't carry self-published books.
Books from the big publishing houses, on the other hand: those are findable. They are promoted by marketing professionals, and they land on the shelves of local bookstores, national chains, and libraries. They might fizzle and die, but even the least-promoted titles still enjoy more visibility than I could ever achieve on my own.
So now I wait a while, weeks or months, to see if this agent will represent me, If not, I have a fallback plan that involves the Doppler radar and a tinfoil hat.