Q: calendar on iMac not updating from phone

You likely don't have iCloud set up correctly. Please look over http://www.apple.com/icloud/setup/ , once you have iCloud set up on both devices ensure you are looking at the same calendar on each device. For example, you can have calendars for yourself, holidays, a significant other, etc...

1. Calendars in the On My Mac or On My iPhone/iPad/iPod category, and calendars that sync with other network services such as Google, will not sync with iCloud.

2. Please back up all data, then take all the applicable steps in these support articles:

          iCloud: Troubleshooting iCloud Calendar

          iCloud: Advanced Calendar and iCal troubleshooting

Nearly all sync issues should be resolved that way. Please make sure you've taken all the steps and tested adequately before continuing.

3. If there are any calendars on your Mac that you don't synchronize with iCloud, export them by selecting them in the calendar list and then selecting

          File ▹ Export ▹ Export…

from the menu bar. Quit Calendar.

4. Triple-click anywhere in the line of text below on this page to select it:

~/Library/Calendars

Right-click or control-click the highlighted line and select

          Services ▹ Reveal

from the contextual menu.* A Finder window should open with a folder selected. Move that folder to the Desktop.

5. Launch Calendar. Your calendars will initially be gone, but they should resynchronize with iCloud. If they don't, uncheck the boxes marked Calendars and Reminders in the iCloud preference pane, then re-check them.

6. Import the calendars you exported in Step 3, if any, by double-clicking the files.

7. If the issue is resolved, close the Finder window you opened in Step 4. Delete the exported files and the Calendars folder on the Desktop.

*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combination  command-C. In the Finder, select

          Go ▹ Go to Folder...

from the menu bar and paste into the box that opens by pressing command-V. You may not see what you pasted because a line break is included. Press return.