A "Private Channel" is defined by the system owner for that use and may not be any more "private" than any other of their channels, depending on how they set it up. It may simply be a secondary channel that normally doesn't have much traffic and therefore be "private". This channel may be a seperate frequency (on the same band or even on a different band that they may have kept as a backup or for special operations, training, or just because the department would rather let the license expire than give it back to the FCC (you never know when that old low-band VHF frequency will come in handy!).
It may be a simplex channel so it has much less range than their normal repeater channels, so it would be "private". It may be a channel that is only programmed on a select few radios to allow "private" conversations to happen (you've gotta have someplace to plan the Chief's surprise birthday party!). It could even be on one of their normal channels, but use a different PL tone to make it "private". In these cases, a simple scanner can probably pick up this "private channel" if you're within range.
A "Private Channel" could also be a special encrypted channel, or could be code for "call me on my cell", which would make it actually "private" since scanners wouldn't pick them up.
If you're asking about a certain agency's "private channel", you can name the agency and folks may know which of these may apply to them.
