Lockin amplifiers are the coolest instruments in the world
I have a few of that model sitting around, although most of them don't work any more.
A lock-in amplifier measures the amplitude and phase of a signal at a specific known frequency. It multiplies the input signal by a sine wave at the known reference frequency. Through the normal non-linear conversion process, this generates sum and difference frequency components. For the special case of the component of the signal that is at the same frequency as the reference oscillator, the difference frequency is at 0 Hz or DC. That signal is filtered with a low-pass filter, and produced as a slowly varying voltage or displayed on the meter.
The magic is that the analog multiplier followed by a low-pass filter is equivalent to a bandpass filter with the same bandwidth. This is nice because it is easy to make a 0.01 Hz lowpass filter, but quite difficult to make a bandpass filter centered at 5 kHz, but with 0.01 Hz bandwidth.
The second important point is that the lock-in measurement is phase sensitive. For any given frequency you can have a sine wave or a cosine wave, and they are distinct. A single-phase lock-in measures only one, the component in phase with the reference signal (they will have an adjustment to change the reference phase to match the signal). A dual phase lock-in measures both the sine and cosine terms independently. This is how most LCR meters work: they inject an oscillating voltage and measure the conducted current with a dual-phase lockin. The in-phase term gives the resistance, while the out-of-phase term gives the reactance.
Lockin measurements come in many guises, but in many ways they are a much more sophisticated cousin of a 'relative mode' measurement. If you are trying to measure a small voltage with a DMM, you can compensate for the DC offset by in turn shorting the probes together and connecting them to the source you want to measure. Subtracting the background reading from the signal, and you eliminate the offset error in your DMM -- as long as the offset doesn't drift in the time it takes you to switch measurements. By hand you can only switch the signal at 0.25 Hz or so, but a lockin amplifier can work at 10 kHz.
A classic lockin use is to measure an optical signal in the presence of a huge background noise. If you are trying to use a photodiode to measure the amount of light from a laser pointer scattered off a wall in broad daylight, you might expect it is impossible. The sun is orders of magnitude brighter than the little laser pointer. However, if you use an optical chopper to block and uncover the laser at a few kHz, a lock-in amplifier can recover the signal in the presence of much larger noise.