Lyophilization, vacuum freezing or freeze-drying is a method of drying.
Such a simple definition that explains a lot about a word that the average person has trouble pronouncing. It is simply a way of drying something - getting rid of the water. Conventional hot air drying is familiar to everyone, as is arbitrary drying (e.g. clothes on a line).
When it comes to food, the latter method, with a few exceptions, doesn't work. As a rule, food spoils before it dries. These exceptions include, of course, drying mushrooms in the attic or Indian meat (jerky) dried in the wind (with the help of salt). Either way, it is always and only a matter of evaporating water from the dried food, and this is no different with freeze-drying.
The fundamental difference is in the conditions under which the water evaporates. The fastest evaporation method is boiling at 100°C. However, this temperature is not very gentle on the food - anyone who has ever left a pot on the stove for too long knows the result. That's why you need to lower the temperature.
However, if we lower the temperature, for example to room temperature 20°C, we do not get boiling and evaporation takes too long again. That's why we also need to reduce the pressure. Even at high altitudes, water can boil at 80°C. If we reduce the pressure even further, down to 6 mbar, the water can boil even at 0°C. This is the so-called triple point, where water will boil, freeze and be liquid at the same time. Our goal is to get the water from the solid state (ice) straight into the gaseous state (steam), leaving out the liquid phase.
If we have food frozen to about -20°C and the vacuum around it is close to vacuum, the desired evaporation of water occurs, which in this case is called sublimation (from ice straight to steam). To speed things up, we can now do the same thing we did with the stove - heat the product a little more to get closer to the boiling point. The water will start to leave the food quickly.
The water needs to be captured somewhere. This is taken care of by the condenser, which needs to be at a much lower temperature than the dried food. It's basically the same principle as when you put a glass of chilled water on the table - it will immediately dew as it draws moisture from the surrounding air onto itself.
When the food is dried for a long enough period of time, the water content is reduced to just one percent. Then comes the second stage - secondary drying. This is the capture of the last free water particles in the product chamber. As the water is no longer in the food, the product temperature can be raised to plus values between 30 to 40°C at this stage.
After that, all you have to do is stop the process, return the pressure to ambient level and remove the dried food from the chamber. The freeze-dried product is extremely dry and to keep it that way, it must be well wrapped and kept out of the air.
This is probably simpliest explanation of how food lyophilization works. If you are looking for more advanced source, please check article Basic Principles of Freeze-Drying by John Barley from ATS.