Compact model refers to modeling of current-voltage behavior electron device (like MOS transistor) using a set of equations and parameters. It is used for circuit simulation of integrated circuit (IC). Since the fabrication cost and time of IC chip is large, IC designers need to simulate the circuit function before hand out the layout of IC to fabrication company. So it need to be accurate. And, since the IC scale is large (billions of transistor in Intel newest CPU), the model need to be sufficiently simple. It is also referred as SPICE model, since most of the circuit simulators are based on SPICE language (https://en.wikipedia.org/wiki/SPICE).
Another model used in semiconductor field is physical model, or TCAD model. It can simulate the physical properties inner the electron device, like charge densities, electronic potential distribution, and also the current-voltage output, based on the physical rules of electron transport. It's a powerful tool to analyze the performance of the device and the physics behind it. However it's very time consuming, even for a single device.
Compact model is like a black box of the electron device. It doesn't care what happen internal, and only gives the output behavior of the device (current and voltage responses on its terminals). I don't who invented the phrase "compact model" and why. I think this might be what the word "compact" refers to.