Magnetic dip refers to a behavior of magnetic compasses. Magnetic compasses do not directly indicate the magnetic north pole; rather, the magnet in them aligns itself with the lines of force that make up the Earth's magnetic field. As a result, they are rarely aligned completely horizontally. As the compass is taken further to the north, the 'dip' - the angle below horizontal which it indicates - will increase.
Most magnetic compasses are designed with a 'card' (really more of a part-globe) as the moving part. This card is balanced at its inner top atop a pin to allow it to spin freely. That usually will allow it to tilt left and right to some degree as well to compensate for dip. However, the design of the compass will generally mean there is a limit to the degrees of dip the compass can take and still function. In an aircraft, a banked turn of over 20° or so will cause the compass to 'lock up' as it tilts too far and contacts the sides. This is why making turns using the magnetic compass - compass turns - is a different proposition from using the heading indicator, and is why the latter is in the airplane in the first place.
Back to magnetic dip. Magnetic dip is also indirectly responsible for ANDS - the tendency of the compass in the northern hemisphere to indicate a turn northwards under acceleration along an east/west line, and a turn to the south under deceleration. In order to compensate for magnetic dip, compass makers generally place a small weight on the side of the card opposite the nearest pole - so, in the northern hemisphere, it's placed at the 180° mark. This will 'tilt' the compass card back towards level and make it usable over a wider range of latitudes and hence dip angles. However, it means the compass card 'masses' more on the anti-pole side. So when the aircraft is accelerated, the heavier side will usually move towards the back until the force of acceleration is removed. If the heavier side is on the south, then the compass will spin towards the south - indicating a turn to the north. Deceleration is the reverse.