Extra information that only exists attached to something else — an icon, an avatar, a tab label — and isn't clickable or removable on its own. A numeric badge needs accompanying text for screen readers, like "3 unread messages" (the bare number "3" carries no meaning alone), while a purely decorative dot should be hidden with aria-hidden="true".
Often confused with a chip, but independence is the difference. A badge always rides on top of something else and is never clicked by itself, while a chip is a standalone element you can click or remove on its own.
Once the count runs past two digits, capping it at something like "99+" is conventional — the badge has little room, and three digits would swallow the icon underneath it.