The auxiliary field, H is defined from the magnetic field B, the magnetization M and the permeability of free space μ₀.

Confusion sometimes arises because the H field was named the magnetic field or magnetic field intensity in the past, while B was denoted as the magnetic flux density or magnetic induction. Similar to Thermodynamics, where we can talk about macroscopic phenomenon and solve problems without dealing with microscopic properties, the H field is a macroscopic field like the electric displacement D.

References

[1] Magnetic field, Wikipedia

[2] Jackson, D. ”Classical Electrodynamics”, John Wiley and Sons, Inc., 1975.

[3] Griffiths, D. ”Introduction to Electrodynamics”, Prentice-Hall, Inc., 1999.