iPGMail is an iOS low cost encryption app based on OpenPGP, an open source implementation of the data encryption program Pretty Good Privacy (PGP). It has no backdoor and it is used by corporations protecting trade secrets and people whose opponent is an entity or country with large resources. Even for a spy agency, there is no way to break OpenPGP encryption other than guessing or stealing the password and encryption keys.
You can use iPGMail to encrypt and digitally sign email and files. Encryption keys can be imported if you already have them, or you can create them in the app, designating a few configuration options like key size and expiration date.
Like all public key encryption schemes, you will need the encryption key of the recipient you are sending mail to. iPGMail is able to search various public keyservers where to download other people public encryption keys from and upload your own to the server for others to find. Another option is to get iPGMail to automatically attach your public encryption key to messages you send.
The iOS mail application will automatically pass PGP attachments to iPGMail for processing but when selecting to send encrypted messages as text pasted in the main body, rather than as attachment, then you will have to copy and paste the received encrypted text into iPGMail to decrypt it.
You can choose for email messages to be only encrypted, only digitally signed or encrypted and digitally signed at the same time. When an email message is decrypted after entering the correct password, two bars on top of the application will turn green to let you know that encryption and digital signature verification were both accurately executed.
iPGMail can also be used to encrypt files, like documents, photos and videos. Those files can be send attached via email or distributed uploading them to Dropbox or iCloud. iPGMail can link up your Dropbox account inside the application and give you access to your Dropbox folders without leaving the program.
Encrypted files will have the extension .pgp, and can only be deciphered by those whose public key encryption has been used to secure them. To protect against someone accessing your encrypted messages, if you lose your iPhone or iPad iPGMail times out the cached password when you are not using it, and optionally, it can also password protect the app with a PIN number.
One of the beautiful things of OpenPGP based programs is that encrypted data can be deciphered in any other operating system. A free program tool to do that on a Mac desktop computer is GPGTools, on a Windows OS it can be done with GPG4Win, Unix computers can use GnuPG and Android users APG. To be able to exchange encrypted messages with your friends they will not need to have the same app or operating system installed, any of the free applications mentioned above will suffice to securely correspond with you.
I you only want to encrypt files you can find better applications, but to exchange encrypted email in iOS, iPGMail is most likely the best solution. A similar iOS app you might want to look at is oPenGP.