If you have more than one email, calendar, contacts, notes or reminders account on your phone, you should tell your device which one you want to be the default one lest your calendar entries or contacts get saved to the wrong account. In a typical scenario, let's say you have a personal iCloud account and an account for your work. If you don't set your default accounts properly, you may end up putting business meetings on your personal iCloud calendar or personal contacts in your business address book.
Typically, unless you have a specific reason for doing so, your default account for mail, contacts and calendars should be the same account, though it doesn't have to be.
To set your default accounts, head to settings from your home screen.
Scroll down and look for Mail, Contacts, Calendar, Notes and Reminders.
Start by tapping on Mail. Swipe to the bottom and tap "Default Account." Select whatever mail account you want new emails to go out of by default. You can always change this when sending an email. (See below.)
You'll repeat this process for Contacts, Calendars, Notes and Reminders. You'll need to select settings >> Contacts, Settings >> Calendar and so on. Note that each is in a slightly different location (see screenshots below). Also, if you don't see a "default account" option, it simply means you don't have more than one account with that service enabled. For example: if you don't see a "default account" under "Calendars," it just means you only have one account with calendars turned on.
Once you've specified your default accounts, you can still send and save to other accounts. Here's a how-to:
How to email from an alternative account
Creating a contact in something other than your default contacts account.