Plain English Meaning
The compass needle doesn't just point sideways toward the magnetic pole — it also gets tugged downward toward it. That downward tug makes the compass give wrong readings when the airplane banks in a turn or when it speeds up or slows down.
Full Definition
Dip errors are inaccuracies in the magnetic compass caused by the vertical component of the Earth's magnetic field pulling the compass card downward toward the nearer magnetic pole. This vertical pull tilts the card during turns and during changes in airspeed, producing two specific errors: turning error (most pronounced when turning to or from north or south headings) and acceleration/deceleration error (most pronounced on east or west headings).