Ponder refers to thinking in the opponents time:

• To use the opponents time, to continue searching the tree and store the information in a large lookup table for later use.
• This will save time when its our turn.
• Requires transposition tables.

While the opponent is looking for a move, instead of sitting idle, guess their most likely move and start analyzing the resulting position.

• If we guess right, we have a head start searching;
• if we guess wrong, we have wasted no time and will have at least somewhat populated the transposition tables.

More useful against humans, and engines running on separate machines.

• On the same machine, each engine will disrupt the other with their pondering efforts, resulting in a lot of noise.