If you specify another user as a Delegate on your calendar, you have the option of selecting who will receive the invites to your calendar on your behalf. You can choose to receive these yourself, or you can set your delegate to be able to receive and reply to them instead. By default, Outlook gives this power to your delegate, which is not always ideal!
To disable this, you can use the following steps:
1. In the Outlook Web Application, right-click on your Calendar and select Sharing Permissions
2. For the Delegate, you should see the option to "Send invitations and responses to:" with a drop-down. Click on this drop-down and select "Both my delegate and me" which will ensure you also receive notifications.
You can change permission from Delegate to Can Edit if you want to remove their ability to see calendar invitations, but still give them the ability to make edits to your calendar.
You can read this article by Microsoft Support on Delegate Permissions in Outlook.