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I'm confused between them. Can someone explain the difference between them? Is $\vec H$ field ONLY relevant during magnetization or demagnetization? $\vec H$ is just that value needed to magnetize/demagnetize or what is it useful for?

Is $\vec H$ only relevant to solenoids or magnets as well? Does it make sense to state a magnet has a field of $0.5T$ and a field strength $\vec H$ of $9\times10^5 A/m$?

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Look at the definition of $\vec{H}$. It is equal to $\vec{B}/\mu_0-\vec{M}$ with $\vec{M}$ the magnetization. Its main use comes from the fact that $\vec{\nabla}\times\vec{H}=\vec{J}_{free}$. Seeing as we are usually only able to accurately control free currents (as opposed to induced ones in the material), this formula is quite useful.

Note that, outside of a material (in the vacuum), $\vec{H}=\vec{B}/\mu_0$, so if you like you could use $\vec{H}$ in all of the equations where you'd normally use $\vec{B}$, getting rid of the usual factor $\mu_0$ that appears virtually always when dealing with magnetism. For a much more elaborate explanation, look at chapter 6 of Griffith's standard undergrad textbook.

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(you can write \vec{J}_\text{free} there, or \vec{J}_\mathrm{free}) –  NikolajK Nov 21 '13 at 10:19
    
@Danu I believe I'm starting to understand...B is usually used as the external field, and H being the field produced by a material. So, they all represent the magnetic field. –  M. A. A. Nov 21 '13 at 10:32
    
@Danu B & H exist at the same time? Is H considered to be a force? It's sometimes called magnetization force, if so is 9x10^5 A/m a lot? And could it be compared to normal force? –  M. A. A. Nov 21 '13 at 19:16
    
Why don't you work out what that would be in terms of a $\vec{B}$-field, taking into account the $1/\mu_0$? In terms of how to interpret $\vec{H}$, I'd say: work out its units! Check, for instance, whether it has the same units as force... –  Danu Nov 21 '13 at 19:32
    
@Danu Well, it's more a field than a force. Looking at the unit it shows that... H is noted magnetization force, but not sure why. What do you think? H is a field or a direct force? –  M. A. A. Nov 22 '13 at 6:33
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