The doctrine of privilege allows you to refuse to disclose documents to the court and to refuse to answer certain questions even when those documents or questions are relevant to the case.
There are two main types of privilege:
You have a "privilege against self-incrimination". This means that you can refuse to answer questions or hand over documents that may implicate you in criminal proceedings.
You may have a "legal professional privilege". A legal advisor and his or her client cannot be forced to disclose communications between them.
In addition, if any communication is made in contemplation of litigation (i.e., with a court case in mind), then that communication is privileged even if it is not a communication between lawyer and client.
Priests are allowed to refuse to answer questions relating to what was said in the confessional. This is known as the "sacerdotal privilege". Similarly, communications with a counsellor may also be privileged.
This is privilege claimed by the State. In some very limited circumstances, the State may refuse to disclose information or documents in order to protect the public interest. For example, documents relating to the structure and engineering of army equipment might be held to be privileged in order to protect national security.