|A family Bible, from Wikipedia|
When writers talk about story bibles, they mean a place to collect all the information that pertains to the story. The notion comes (I believe) from episodic television where the producers had a document describing the situation and all the characters. They would give it to the writers brought on to pen different episodes so that the scripts they produced had a degree of consistency (e.g., you wouldn't want a character who is normally shy and retiring leap out to save the day in one episode and then go back to hiding under the table in the next).
When software architects design commercial data systems, they are careful to create a single source of truth. A story bible is really nothing more or less than this. It can be physical, like a folder or a binder (bound books are probably not suitable because you'll want to add, remove, and arrange your material), or virtual (anything from a text file to a database, depending on your ambition). All that matters is that it's the one place where you can keep everything related to your story.
Don't let the word, "bible," frighten you with visions of formalities with which you must comply. You'll probably come across suggestions that you subdivide your bible into sections on characters, settings, backstory, and so on. Those are reasonable but not the only ways to organize your material. You could also organize your story bible like an encyclopedia, with entries for each significant entity in your story. All that matters is that you have a way to organize your material so that 1) you can easily find it again, and 2) you know where to add new material.
Remember, this is your resource, so the only thing that really matters is to find something that works for you.
And, in the spirit of our recent discussion about writers who over-plan, don't let the bible become something that takes so much time to maintain that you have no time left to write the story. Promise yourself that the bible will forever be a private document, the information equivalent of what you look like when you get out of bed in the morning, so you're not tempted to try to make it presentable.
The good folks at The Write Thing have a thorough discussion of what you might want in a writing bible if you'd like more.
Deren Hansen is the author of the Dunlith Hill Writers Guides. Learn more at dunlithhill.com.