On an Android phone, notifications appear in the lock screen of your phone. When you click on it it will not open the notification but bring you directly to the app.

If the text of the notification is longer than the text window Android is providing you see only parts of it in the preview.

1) In order to read the whole notification (sometimes you can only see parts of it as the text is longer than the window allows showing) on the locked screen, please tap on the text with your finger and then pull it slightly down. You will then be able to read the complete text.

2) In order to be able to read it (again) after the screen has been unlocked, please go to the message center at the top of your phone's screen. There, tap on the text and slightly pull it down to read the whole text.