What is meant by a #"good solvent"# for recrystallization?
It means capable of dissolving and recrystallizing stuff.
The normal means of purification of a compound are by recrystallization. Ideally, (which things never are!) a solute should be quite soluble in hot solvent, and poorly soluble in the cold solvent, so that on cooling the bulk of the solute crystallizes out. Both alcohols tend to fulfill these criteria with regard to recrystallization of many organic species.
Why should the solvents have these properties? Well, both alcohols give you a large, useful temperature range. Methanol and ethanol boil at
Both alcohols are also cheap. Methylated spirit (which is ethanol denatured with a bit of methanol or phenol or some other denaturant so that you can't drink it) is dirt cheap, and used industrially in vast quantities. Finally, at least in the case of ethanol, it smells nice, and does not dry out your hands.
Here is a question for you to consider. Hexanes and ethanol are infinitely miscible. What does this mean? Hexanes and methanol are IMMISCIBLE. Why?