Your iPhone is an especially vulnerable device. It contains heaps of personal and company data, it roams from wifi to wifi, and it is small which makes it easy to lose (or steal). Yes, it is unlikely that there are people out to get you, but it is certain that there are people out to get whomever they can. You do not lock your door to keep out assassins, you lock your door to keep out opportunists. These are two things you can do to make your iPhone and yourself more difficult targets.
Security certificates are a way for your phone to verify that a server responding to a certain domain name is authorized by the owner of that domain. When your phone alerts you of certificate issue, it is trying to tell you that the server your phone is connecting to is not passing this verification process. This alert is the iPhone equivalent of "Stranger Danger!"
It is within the skill set of a thirteen-year-old to construct a wifi network that will pretend to be any email server your phone tries to reach and collect a list of the servers, email addresses, and passwords that your phone passes to it. Fortunately, your phone attempts to verify the identity of the server before it attempts authentication. This gives us a chance to deny the bored thirteen-year-old hacker access to your email.
If you see an error like the "Cannot Verify Server Identity" notification above, please click "Cancel."
This Phone will Self-Destruct
OK, not really destruct, but self-erase. This setting will restrict the ability of someone who finds or steals your phone to gain access to your data. Consider the damage such access could do. Not only would such a person be able to read and copy all of your emails, notes, contacts, and photos, that person could very effectively pretend to be you to all of your contacts. This setting, found at the bottom of Settings > Touch ID & Passcode, configures your iPhone to erase itself after ten unsuccessful unlock attempts. You may remember a dispute between Apple and the FBI. This setting was involved.
With the Erase Data setting enabled, I cannot recommend strongly enough that you make regular or automatic backups through iTunes or iCloud. Also, you must enable a passcode, but I almost thought that suggesting a passcode could go without saying. Almost.
Back up your phone, then set it to erase itself if someone tries to break in.