Solubility

The solubility of a substance is the maximum amount that will dissolve in a given volume of solvent.  

Solutions are said to be saturated when the maximum amount of solute is dissolved in the presence of excess solute. 

The solubility curve shows that solubility depends on
 
graph


the chemical nature of the solute
The graph shows that different solids have differing solubilities at a particular temperature.
 
the chemical nature of the solvent
The substances in the graph would have a different solubility in a different solvent such as ethanol.
 
the temperature
Most substances are more soluble in hotter water.
The graph shows that the extent to which solubility changes with temperature depends on the chemical nature of the solute.

The examples in the graph are ionic solids.  Many, but not all, Ionic solids are water-soluble.

Ionic solids that are insoluble generally have highly charged cations and/or anions. 
For these solids, the attractive forces between the ions in the solid are greater than the attractive forces between those ions and water.