Difference between parallel adder and serial adder when adding two binary numbers
If you want to add two N-bit numbers, a parallel adder will use N copies of a full-adder circuit, and it will produce a result in one clock cycle.

On the other hand, a serial adder will use just one full-adder circuit, but it will require N clocks to produce the result.

The tradeoff is circuit complexity (and power consumption) vs. time.

Some examples: A desktop PC uses a parallel adder, because it wants to be able to do as much arithmetic as possible in a given amount of time, and there is no real restriction on how much power it can consume. On the other hand, a handheld calculator only needs to be as fast as the human operating it, but it needs to last a long time on a small battery, so it uses a serial adder.