What is the term for the general principle that solubility is greatest when the polarity of the solute is similar to that of the solvent?
How about "like dissolves like"?
This is a commonly-used tool to help remember a general rule about solubility and polarity, and it essentially means that polar solvents best dissolve polar solutes, and nonpolar solvents best dissolve nonpolar solutes.
This is visually illustrated in the case of oil-and-water;
Oil is made (at least mostly) of long hydrocarbon chains called fatty acids, which are nonpolar, and water is a very polar molecule...and do they mix?