Saturated Solution
A saturated solution holds the maximum amount of dissolved solute possible at that temperature; any additional solute settles out undissolved.
Definition
A saturated solution is one that cannot dissolve any more solute; if you add more, it just sinks to the bottom. It contains the maximum concentration of solute that can dissolve at a given temperature and is in equilibrium with any undissolved solute, whereas an unsaturated solution can still dissolve more and a supersaturated solution holds more than the normal limit, usually because it was cooled slowly from a hot saturated solution. Warming a saturated solution usually lets more solid dissolve. In a saturated solution the rate of dissolution equals the rate of crystallization, a dynamic equilibrium in which solute particles continually leave and rejoin the solid with no net change, so the dissolved concentration equals the solubility at that temperature and pressure; a supersaturated solution is metastable, and a seed crystal or scratch provides a nucleation site that triggers rapid precipitation back to saturation.
Example
Keep adding sugar to a glass of water and stirring, and at some point the sugar stops disappearing and piles up on the bottom: the water is now saturated. At $20^\circ\text{C}$, $100\text{ g}$ of water saturates with about $36\text{ g}$ of $NaCl$, so a solution with $30\text{ g}$ is unsaturated, and if you add $40\text{ g}$ about $4\text{ g}$ stays on the bottom no matter how long you stir. Sodium acetate dissolves to about $124\text{ g}$ per $100\text{ g}$ of water at $20^\circ\text{C}$ but far more near boiling, and a solution prepared hot and cooled undisturbed remains supersaturated until a single crystal is dropped in, after which it solidifies within seconds and warms noticeably, the principle behind reusable hand warmers.
Key Insight
Saturated does not mean thick or syrupy, it just means full; a saturated salt solution is still thin and clear. Rock candy is made from a supersaturated sugar solution, and as it cools the extra sugar has nowhere to go and slowly crystallizes on a string. Saturation is defined at equilibrium, so it is a thermodynamic limit rather than a kinetic one, and a solution that looks "done dissolving" after a minute of stirring may still be far from saturated if dissolution is slow.