Usually, when you interview someone for a story, the mutual understanding is that anything that is said may be used for publication in some fashion. The interview, as standard practice, is on the record.
Sometimes, however, a source may want to provide information with the understanding that it will not be published. They want to go off the record, to provide background information, give a heads-up, speak frankly about a subject or any other reason.
This is perfectly fine. If a source wants to go off the record, and you feel doing so will not harm your ability to report a story, you may do so. Turn off your recorder, stop taking notes and listen. Just make sure you are clear about when you’re back on the record.
Note that going off the record is a mutual agreement. A source cannot tell you something, then retroactively claim it was off the record. An interview with a reporter should always be assumed to be on the record unless an explicit, mutual agreement is made.
When in doubt, consult your editor or Collegian administration.