There are some instances where you wish to map alias email addresses to an account in Office365 (Office Online).
On one of my SharePoint installations, I was having a ton of issues with SharePoint Search. I had created a SharePoint Search Application post-install with a different service account. The search application starting adding an additional 10 MB to the individual log files. I would reset the IIS application pool, but would see the search application continuing to run.
In instances where your network administrator has created an external trust with another domain, you may want the SharePoint People Picker to find users in the external AD.
According to Microsoft’s TechNet, “The People Picker automatically issues queries to all two-way trusted domains when it uses the application pool account to search for users and groups. When you select a secondary account in the People Picker, the primary account information will be returned.” Therefore, by default two-way trusts are automatically searched.