Does "a signal is buried in noise" mean that the noise amplitude is still smaller than the signal amplitude? (Special case: Lock-in amplification)
What you're missing is the bandwidth, both of signal and noise.
If you look at, let's say, a 1 V rms sinewave signal, together with 10 V rms noise on an oscilloscope, you'll see only noise.
However, if the noise occupies a 1 MHz bandwidth, and is flat with frequency, and you pass the signal + noise through a 1 kHz bandwidth filter centred on the signal, then you will eliminate 99.9% of the noise power, dropping its amplitude to 0.3 V rms. The signal will then be clearly visible.
A lock-in-amplifier is a neat way to make a very narrow filter centred on the frequency you feed in as the reference.
You can use the same principle even without sine waves. Spread spectrum systems like CDMA and GPS use a pseudo-random square wave signal as the reference, and call the 'multiply and average' process convolution or correlation. As long as the reference is is the same as the underlying signal, and as long as the averaging process produces an effective bandwidth small enough to drop the noise power, the signal can be 'dug out of the noise'. A lock-in-amplifier is a special case of the more general 'correlation with a reference' that's used for CDMA.