So-called freeze distillation is a metaphorical term for a process of enriching a solution by partially freezing it and removing frozen material that is poorer in the dissolved material than is the liquid portion left behind. Such enrichment parallels enrichment by true distillation, where the evaporated and recondensed portion is richer than the liquid portion left behind.
Such enrichment by freezing of a solution in water is sometimes oversimplified by saying that, for instance, because of the difference between water's 0°C freezing point and ethyl alcohol's -117° one, "the water freezes into ice ... while the ethyl alcohol remains liquid". This is false, and although some of the implications of that description are true and useful, other conclusions drawn from it would be false.
The detailed situation is the subject of thermodynamics, a subdivision of physics of importance to chemistry. Without resorting to mathematics, the following can be said:
Freezing in this scenario would begin at a temperature significantly below 0. The first material to freeze would not be water, but a dilute solution of alcohol in water. The liquid left behind would be richer in alcohol, and as a consequence, further freezing would take place at progressively lower temperatures, and the frozen material, while always poorer in alcohol than the (increasingly rich) liquid, would become progressively richer in alcohol. Further stages of removing frozen material and waiting for more freezing will come to naught once the liquid uniformly cools to the temperature of whatever is cooling it. If progressively colder temperatures are available, the frozen material will contain progressively larger concentrations of alcohol, and the fraction of the original alcohol removed with the solid material will increase. In practice, unless the removal of solid material carries away liquid, the degree of concentration will depend on the final temperature rather than on the number of cycles of removing solid material and chilling. Thermodynamics gives fair assurance, even without more information about alcohol and water than that they freely dissolve in each other, that even if temperatures somewhat below the freezing point of ethyl alcohol are achieved, there will still be alcohol and water mixed as a liquid, and at some still lower temperature, the remaining alcohol-and-water solution will freeze without an alcohol-poor solid being separable. In practice, while not able to produce an alcohol concentration comparable to distillation, this technique can achieve some concentration with far less effort than any practical distillation apparatus would require.
Today, freeze distillation of alcoholic beverages is illegal in many countries, as it carries certain health hazards - a number of unwanted by-products of fermentation (which are mostly removed by heat distillation) tend to accumulate in freeze-distilled beverages to an unhealthy level.
The best-known freeze distilled beverage is probably applejack. Ice wine is the result of a similar process, but in this case, the freezing happens before the fermentation, and thus it is sugar, not alcohol, which gets concentrated.