The simple definition of publishing a book is to make it available for the public to consume and read.
You can publish a book as an online e-book. Simply convert your manuscript into an e-book format and sell it online.
You will have to find a reputable literary agent to represent you if you want your book published by a major publisher.
When you self-publish traditionally, you have to prepare your book files (cover and text), get an ISBN number, have a certain number of your books printed and then ship them off to customers and distributors.
You can self-publish your book online using print on demand (POD) services. When someone orders your book the book is produced and shipped to the customer automatically.