First is the subject. This is what got Private Manning in trouble. Near as I can tell there weren't any real "secrets" in the information that he gave to Wiki-Leaks, the whole point of the secrecy is that the "enemy" did not know what our intelligence people were studying. We may not know anything about our subject, but just knowing who or what the subject is would be valuable for the enemy. Do we even know who they are?
Second is traffic. An outside observer might be able to detect an increase in message traffic, even if the content of the messages themselves are unreadable. Detection could be done by counting the number of carrier pigeons, or watching the electric meter at a computer facility, or if you have access to the actual channel, by counting the number of messages being sent. This one is fairly easy to subvert, all you need to do is to fill all channels with dummy messages all the time. Still, an increase in real message traffic is liable to cause an increase in real world activity somewhere, so just watching the comings and goings at military bases and embassies might tell you something. Yeah, like the ambassador is throwing a party tonight. Whoopie.
Third is the content of the message. There are a multitude of methods for preventing messages from being read by unauthorized personnel, and there are just as many methods for cracking them. Computer encryption is subject to computerized decryption. It may take a while, but with enough computers on the job it becomes possible. Conversely, the more secure the method, the weaker it is. Only one person knows how to decrypt the message? Corrupt that one person and you have access to the message.
Lastly, there is the network. This is what the NSA is after with all the phone records. Some people are worried that their phone calls are being monitored. Someone who has something to hide from the NSA is not going to be speaking "in the clear", they are going to use jargon and code words to communicate. No, what the NSA and most other intelligence agencies want to know is WHO you are talking to, not what you say. This one is difficult to foil, though I am sure it can be done. This is why people in the movies are always using "burner" (pre-paid) cell phones and replacing them on a regular basis. Bought with cash, there is no record of who buys a "burner" phone. Shoot, I wouldn't be surprised if the first thing the NSA did with all those phone records they got was to eliminate all the phone records for phones where they knew whose phone it was. No self respecting terrorist would use their own phone for any kind of operational communications.