Good explination SleazeyWombat.
In order to transmit radio waves any significate amount of distance, you need two things:
Power and High Frequency.
In order to send out a radio signal (such as reporting a contact to BdU, etc), you have to take the information (IE Voice / telegraph) and modulate it with another frequency that is higher than the information known as a carrier wave(our voices go from about 20 Hz to 14 Khz and a telegraph is only so many pulses per second). So a transmitter will have an oscillator and a mixer, the mixer mixing the two together. This is nomally called modulation, and you can modulate something either in Amplitude (AM radio) or in Frequency (FM radio).
Once you have your modulated signal, you can now amplify it to give it power and out the antenna it goes (I realize this is a GREATLY simplification of the process, but enough to make one understand what is happening).
You will have a receiver so that you can hear what is being sent back. The way a receiver works is backwards from the the transmitter: receive and amplify the signal. Mix the signal with another signal that is 180 degrees out of phase with the incomming signal. This basically strips the carrier away and leaves you with the information (IE Voice or telegraph) which is then sent to amplifiers and speakers.
Now. Even if you don't transmit anything, if your radio set is left on, you have two problems:
Transmitter's oscillator and the Receiver's oscillator. They are still oscillating and generating energy that can be detected.
Radio silence is just that: silence. Means you must power down your radio equipment.
Any decent detector can see these oscillators, and a radio operator can be trained to sit there and adjust a detector's tuning capabilities to detect any radio energy.
Unless, of course your radio equipment is shielded!
The radar systems I worked on in the Navy, when we went to Radar Silence, it simply meant to redirect the radars RF energy into what we called a Dummy Load (this was a device that absorbed the RF energy instead of letting it out the antenna). All our cabinets had RF shielding around the cabinet doors to keep the RF from leaking out (this is a good thing. Constant exposure to RF energy can lead to ....... health problems!), and can help keep any electronic "ears" from hearing your ship.
Why not just shut our radars down?
Because of warm up time. My radar system, the AN/SPS-48C radar takes up to 15 minutes to be ready to transmit when powered up. It didn't mater if I had just shut it down 5 seconds before. The interlocks on on timing relays that have to time out to 15 minutes before you can bring the transmitter up.
(actually, that's a mis-statement there. The AN/SPS-48C has 4 parts to the transmitter: first stage, second stage, Driver stage, and Final stage. First stage would be ready in 5 minutes, but you'll only see out to 70 NM with it. Second stage would be ready in 10 minutes, but again, you'll not see to far with just it and First stage going. The last two stages, Driver and Final time out at 15 minutes, and you can see over 220 NM with them.).
Whoops.....looks like I'm prattling on again!