The FBI is trying to get a court order to force Apple to create a 'backdoor' that allows the FBI access to the iphone of one of those shooters in California last year.
Apple is saying 'no way' since it's a gross breach of privacy and it sets the precedence for the FBI or other government organizations to do this whenever they want.
Apparently the FBI doesn't even need this information. They're just using this case to set precedence to make it easier for them next time.
Another issue is that if the FBI is granted access to the personal information of iphones, then it means other countries like China will also have the precedence required in order to force Apple to give them access too.
The flip side of this is that the FBI is saying that your privacy should be second to security.
Here's an article on it:
http://www.cbc.ca/news/business/apple-cook-san-bernardino-phone-1.3451372
and here's Apples public response to the FBI's request:
http://www.apple.com/customer-letter/