solubility limit
How much sugar can you stir into iced tea before it stops dissolving and just piles up at the bottom? That maximum is the solubility limit. Add more and you now have two things at once: a saturated solution plus the leftover solid that would not dissolve.
More precisely, the solubility limit is the maximum concentration of solute that will dissolve to form a single homogeneous solution at a given temperature. Below it, one phase; above it, a second phase forms. At about 20 degrees C water dissolves roughly 65 wt% sugar, and beyond that solid sugar remains. In solids the same idea appears as the solvus line on a phase diagram, tracing the maximum solubility against temperature; solubility usually rises as the material gets hotter.
Crossing the solubility limit on cooling is exactly what makes precipitation strengthening work: dissolve solute hot, then cool so fine second-phase particles are forced out to strengthen the alloy. Because solubility depends on temperature, a solution that is perfectly stable when hot can become supersaturated when cooled, ready to shed that second phase.
Water dissolves about 65 wt% sugar at 20 degrees C; stir in more and undissolved crystals stay on the bottom.
The solvus line is just the solubility limit of a solid plotted against temperature.
Solubility depends on temperature (and on which phase); calling something insoluble usually means very low solubility, not exactly zero.