Can you explain both, sql injection or 1=1 ?

The specific question should not be SQL injection OR 1=1 but AND 1=1. There is a big difference here in what the OP is asking about. If I were your teacher and you provided me with JonathanMueller's answer you would get a lousy grade as you dont understand the question.

AND 1=1 is usally used in blind SQL injections. This is when you have to determine between a true or false state from the result of the application to make out what the actual result is. You don't get data listed out in the result, the only thing returned is a state of change. If you try to exploit a Blind SQL injection with OR 1=1 you will fail because the primary use of OR 1=1 is to create an always true statement in order to get the most data out of the database or to force a true statement in the case of a login script being exploited.

A practical blind SQL exploit example:

We use our example: http://www.site.com/news.php?id=7 Let’s test it: http://www.site.com/news.php?id=7 and 1=1 <--- this is always true and the page loads normally, that's ok.
http://www.site.com/news.php?id=7 and 1=2 <--- this is false, so if some text, picture or some content is missing on returned page then that site is vulnerable to blind sql injection.
Another example where you try to figure out MySQL version:
http://www.site.com/news.php?id=7 and substring(@@version,1,1)=4 This should return TRUE if the version of MySQL is 4. Replace 4 with 5, and if the query returns TRUE then the version is 5.
Examples taken from: http://www.exploit-db.com/download_pdf/14475