(you can ignore the t-alcohol)
In order to dissolve something in water, you have to stick the solute in between water molecules that are strongly attracted to each other. This means that the solute should have some compensating attraction for water molecules; in the case of an an alcohol, it's the OH group.
But the non-polar alkyl group does not have any strong interactions with water molecules, and that has to be shoved in there, too.
4-carbon alcohols are just on the alcohol solubility cusp where the size of the alkyl group is getting to be too much for compensation by the attractiveness of the OH group.
Methanol, ethanol and both 3-carbon alcohols are freely soluble in water. The alkyl groups are small enough to squeeze in between water molecules.
No 5-carbon (or larger) alcohol is freely soluble in water. The alkyl groups are too large.
But of the four-carbon alcohols,
This is because the size of the four-carbon group (more specifically, the volume of the four-carbon group) is smallest for t-butyl, and largest for n-butyl and isobutyl.