This application notifies you of new emails instantly even if your mail server does not support pushing emails. Do you want to save battery life? With this utility, you don't need to fetch emails periodically. In your iPhone's settings, select "Manually" in "Mail, Contacts, Calendars > Fetch New Data". This will safe the battery life of your iPhone significantly. After launching this application, create a new account and enter the address of your mail server (for Google Mail, for example, you would use "imap.gmail.com"). In most cases, you'll check "Secure" to protect your data and emails by encryption. From now on, you will be notified of new emails through the push notification service provided by Apple. If you get a notification, simply open the built-in Mail application and read your new email(s).
Please note that if you have more new emails, the preview in the notification will contain the sender and subject only of one of them. Your mail server must support IMAP.
If you don't get any notifications, please check your user name and password and try to switch "Secure" on/off.