The deep web is any web content that is not indexed by standard public search engines. This is an enormous category that includes the vast majority of actual internet content by volume. Your bank account portal, corporate intranets, academic journal subscription content, private cloud storage, personal email inboxes, government databases, Netflix streaming content, hospital patient portals, and social media posts with privacy settings all live in the deep web.
The deep web is not inherently private or anonymous. Your bank account is in the deep web because it requires authentication and is not indexed by Google. It is not private in the anonymity sense - your bank knows exactly who you are and every transaction you make. It is simply not publicly accessible without credentials, which is entirely different from anonymous.
Accessing the deep web requires only the correct credentials or authorization, not special software. You access the deep web every time you log into your email, bank, or any subscription service. Billions of people access the deep web every day without knowing the term for it. Estimates suggest the deep web contains hundreds of times more data than the indexed surface web.