How did a calendar icon make it to my Lock Screen?
This is iOS 8 new feature called Handoff more info here.


  Continuity lets you seamlessly move between your iPhone, iPad, and Mac, or use them together.
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  Use Handoff with Apple apps such as Mail, Safari, Maps, Messages, Reminders, Calendar, Contacts, Pages, Numbers, and Keynote. Start a document, email, or message on one device and pick up where you left off on another device. You can also use Handoff with some third-party apps.