earthelectromagnetism
Usually our compass is hold horizontally, and in the northern hemisphere it will point in the direction of to the north of the earth (actually to the South pole of the Earth's 'magnet').
But looking closer at some points, the magnetic field is not only horizontally aligned but also vertically. So in some point of view, the direction is not the north or the south of the Earth, but in or out of the earth. But does this influence a compass the same as when it is held vertically?
You are correct in saying that the pole near the Arctic circle is really the south pole of the Earth's magnetic field because the north pole of a bar-magnet points towards it. (Wiki)
That said, it is purely convention what you define on a bar magnet to be north and south - we've named the side that points towards the Arctic circle to be the north pole of the bar magnet, and since people don't immediately identify this seeking behavior as opposite poles attracting, we tend to think the earth's field at the Arctic circle is also a north pole when it is strictly speaking, a south magnetic pole.
Also, I would add that the magnetic poles don't coincide with the geographic poles - the latter define the points of intersection of the Earth's rotational axis with the surface of the Earth. We know for a fact that the magnetic poles have shifted (even reversed) with respect to the geographic poles during the history of the Earth. (Wiki)
Earth's magnetic field isn't really a dipole, but a dynamic field due to the convection occurring in the planet's core (consists of molten iron). The model below shows a simulation of the magnetic field (blue is pointing towards the core while yellow points away), the cluster of curves in the middle is the planet's core.
The geomagnetic pole is the location of the pole if earth's magnetic field were a simple dipole (no convection-driven fields).
Note also that, in your image, the geomagnetic pole hasn't moved much in the last century while the magnetic pole has. This is because every several thousand years, the magnetic poles flip sides (a non-constant rate of reversal, so we can't really say a definitive time-frame).
Best Answer
The north end of the compass needle is pulled down towards Earth when you hold it in the normal horizontal position in the northern hemisphere. So much so, in fact, that the south end needs to be slightly heavier to balance it. If you bring that same compass to Australia, the south end, already weighted, will be pulled down even further, perhap even dragging on the base of the compass. So you need to reverse the weights in any compass used in the southern hemisphere.
A chart of magnetic dip contour lines along which the dip measured at the Earth's surface is equal. These are called isoclinic lines.
Magnetic inclination, or dip angle, is the angle that the Earth's magnetic field makes with the horizontal. If you hold the compass vertically in the northern hemisphere, the North Pole end should be pulled downwards.
Image Source: How Magnets Work
A dip needle is just like a conventional compass, but instead of holding it horizontally, it is held vertically. It is a magnetic needle used for navigational purposes just like a compass, but is used predominantly when traveling around the north and south poles. Instead of measuring horizontal magnetic deflection, the dip needle measures vertical magnetic inclination. When over the equator, the magnetic field of Earth is parallel to the surface of the Earth. At the poles, or near them, a conventional compass is very unreliable.