capacitor

The short and simple answer is...

Coupling capacitors are generally used to block DC whiles still allowing and AC signal to pass. Often used at the inputs to AC amplifier stages. DC offsets can be amplified and add up quickly when not blocked out with coupling capacitors. If the DC offset gets too large you will start clipping at the supply rails.

De-coupling capacitors are typically used to short AC signals to ground. They are commonly used at the input power supply pins of ICs. They will both short out some of the AC noise on the power supply lines and they will short the AC noise generated by the IC. If an IC is supplying an AC signal at it's output then it will be drawing AC current at its supply lines. The De-coupling caps keep the AC signal localized to the immediate area and limit the amount that is passed down the supply lines.