Which feature allows users to manage their calendar and schedule from mobile devices?

Exchange ActiveSync is the correct choice because it is a protocol designed specifically for mobile devices that enables users to synchronize their email, calendars, contacts, and tasks with Microsoft Exchange Server. This feature allows seamless management of the user's calendar and schedule from various mobile devices, ensuring they can access and make changes on the go. By using Exchange ActiveSync, mobile users can receive real-time updates from their Exchange accounts, making it easier to manage appointments and meetings directly from their smartphones or tablets.

Other options, while related to aspects of Microsoft's ecosystem, do not serve the primary function of managing calendars directly from mobile devices. Mailbox Delegation pertains to granting permissions to other users to access your mailbox, which is not specifically focused on mobile management. Outlook on the Web is a web-based version of Outlook that allows calendar management but is primarily accessed through a web browser rather than a mobile app. Office Graph is associated with data modeling and analytics, which does not directly involve calendar management.