My Inbox is your personal queue — every conversation where you’re involved, in one place, separate from the shared team view.
It collects conversations that are assigned to you, where you’re a participant, or where a teammate @-mentioned you. Use the filters at the top to switch between these, and to show or hide snoozed and resolved threads.
Work through it top to bottom and you’ll never miss something with your name on it; use Conversations when you want the whole team’s queue instead.