What is a magnetic field? How can the direction of magnetic field lines at a place be determined?

A magnetic field is defined as the space that surrounds a magnet in which magnetic force is exerted.

The direction of magnetic field lines at a place can be determined by finding the direction of the magnetic force on the north pole of the magnet, by using a compass or iron filing.

The needle of the compass gets deflected when it placed near the magnetic field. The north end of the compass indicates the direction of the magnetic field. 

In the iron filing process, iron filings show the shape of the magnetic field produced by a bar magnet by aligning with magnetic field lines.