The global inbox contains information from across the entire network, including hot questions, a list of all sites, an inbox of @responses directed at you, and notifications of badges and ending bounties.
The global inbox (also known as the Stack Exchange™ MultiCollider SuperDropdown™) contains different information representing the entire network, including hot questions, a list of all the sites, an inbox of @responses directed at you via comments and chat, and most recently notifications of badges and ending bounties. You can access the global inbox by clicking on the Stack Exchange logo in the top left corner and browse the different sections via the links at the top of the resulting drop-down.
Use this tag for any questions related to the drop-down global inbox and its functionality. If you have questions specifically about notifications inside the global inbox, you may want to include the notifications tag with your question.