Field lines are a way of modelling a magnetic field. They represent the magnetic flux and the number of lines through a particular area (magnetic flux density, also known as magnetic field strength).
In permanent magnets, there are many small magnetic regions (domains) that all line up. In induced magnets, their domains line up when in a magnetic field.
Domains in hard magnetic materials stay lined up even after removing the magnetic field. In soft magnetic materials, they return back to their original direction.
If you hang a magnet, one end would point towards the magnetic north pole.
The point on the surface of the earth is not the same as the North Pole, which is the point about where the earth rotates. A compass points towards the magnetic north pole, it is a "north-seeking" pole.
Many compasses are weighted so they lie horizontally. The angle between the field line and the line horizontal to the surface of the earth is the "dip". It is a right angle at the north and sound magnetic poles, and zero at the "magnetic equator".
Oersted discovered that there is a magnetic field carried in a wire with current. He found that if the current lines were pointing towards you, the field lines were anti-clockwise.
Magnetic field strength / magnetic flux density depends on:
The magnitude of the current, larger current means stronger field.
The distance from the wire, nearer to the wire means stronger field.
The strength of a magnetic field is measured in Teslas (T).
The strength of the earth's magnetic field is about 0.01mT.
The strength of 1cm of wire with a current of 5 A is about 0.1mT.
A very strong permanent magnet would has a magnetic field of 1T near its poles.
A solenoid is a loop of wire that carries a current. The induced magnetic field travels in straight lines inside it. To strengthen it, add more coils or add a magnetic material inside the core.