What happens
A solution forms when interactions between solute and solvent make dispersed particles thermodynamically favourable under the conditions. Different substances can therefore have very different solubilities in the same solvent.
For many solid solutes in water, solubility increases with temperature, but this is not a universal rule. Each solute-solvent pair has its own behaviour.
What changes the process
Gases often become less soluble in liquids as temperature rises. Increasing the partial pressure of a gas above a liquid generally increases how much of that gas dissolves.
Why it matters
A saturated solution is at equilibrium with undissolved solute under the stated conditions. Adding more solute then does not simply force an unlimited amount into solution.