Subject: What is the H field?

In textbooks on electromagnetism the H field is expressed in terms of the B 
field and then the H field is found for various things like toroidal cores and 
antennas. What exactly is the H field? Is it directly measurable? Does it 
actually exist? In textbooks the H field is found for a toroidal core with an 
air gap. The mathematical expression for the H field contains mu but the H 
field is supposed to be the component (of what?) that is independent of the 
material? I understand what the B field is but exactly what the H field is is a 
mystery to me. Can someone help?

Re: What is the H field?