Iron filings scattered on a card over a magnet do not point at the magnet. They point along the field — each one becomes a tiny compass needle, swivelling to the nearest direction of the magnetic force, and the pattern they make is a picture of the field itself, frozen in a thousand small decisions.
A field line is a curve whose tangent at every point is the direction of the field. There is no such thing as a real line of force in the material world — but the fiction is enormously useful, because a line that starts on the north pole of a magnet and ends on the south pole has to close, and the number of lines leaving a pole is proportional to its strength.
Which is why the lines from two like poles never meet, and why the space between them is empty: a field line has to go somewhere, and it cannot cross another, so it goes round. The filings show you this without being told: there is a bare wedge between the two north poles, and the iron has simply left.
Outside a magnet, the field is exactly the same as that of two point poles a little way apart inside it — a result usually called Gilbert's model. It is not an approximation for a bar magnet, it is an exact identity for the external field of a uniformly magnetised body, and it makes the mathematics possible with a pencil.
Here the field is sampled on a grid and each sample is drawn as a short line in the direction of the force, with the opacity set by the strength of the field. That is precisely what the filings do, which is why the picture looks like a photograph of real filings: it is one.