Edit mode is one of the two states of the dashboard. In the Edit mode you can add and/or remove widgets, and generally do whatever you want with your dashboard. Reporting mode is the state of the dashboard as your client sees it.
You can toggle between the two on the left sidebar.
Besides adding and removing widgets, in Edit mode you can also customize your dashboard (General & Style), add a password to protect your dashboard (Security), add widget sources or archive your dashboard.