If you want to delete Calender block which comes by default installation of moodle from homepage of your moodle based website, follow below procedure,
1. Login to your website as administrator.
2. Go to “Home” page of your website like http://yourwebsite.com
3. On homepage, you will see “Administration” at some sidebar. In that click “Front Page Settings -> Turn editing ON”
4. After this, check the side bar where you see “Calender” block. Click the wheel icon infront of the Calender, and you will see a window like below opened,
5. from this, click “Delete Calender Block”
6. You will be redirected to new page, asking confirmation, so if you want to go ahead with deletion, click “confirm”