In simplest terms, a preamplifier is exactly what it the name sounds like. An amplifier that come before another amplifier.
If you have a source (your computer, sound card, DAP, etc) the output signal coming from it is going to be a signal that represents the audio file you want to listen to. However, because the components that make up the source usually change their electrical properties as they heat up. This is referred to as thermal noise. There is also noise inherent in some components that are used in some sources. All these noises add up and are added to the desired audio signal. If you were to use a straight up power/voltage/current amplifier to amplify the signal that is coming out of the source, you would also end up amplifying the noise that was added to the signal.
A preamplifier is an amplifier that is designed for very low gain but also designed such that it "filters out" the noise and amplifies the desired signal over the noise. The upshot of this is that you end up with a source signal that has not been amplified much (the amplification is on the magnitude of 0-1.5 dB or so, sometimes more), but is now much more differentiable from the noise in the signal. This signal is then sent to a power amplifier which amplifies the signal to much higher levels. Because of the preamplifier in the circuit, the noise continues to be amplified, but remains much less prevalent in the final signal that is sent to the headphones/speakers in question