One example is what TrueCrypt calls plausible deniability. Your drive has an encrypted volume which initially appears to be completely random data (like all well-encrypted data). You have two decryption keys: an "innocent one" and the "real one." If asked or compelled to decrypt your drive, you decrypt it with the innocent one, and it becomes something innocent (like a bare operating system with no personal info). Obviously, the "real key" reveals your real operating system which you actually use, and thus contains personal information.
The kicker is, without the real key, not only can they not see your personal information, but it's physically impossible to even prove that there's another key which decrypts different data on the drive.