There are many documentaries, forums, blogs and more dedicated to Dark Matter. I have been frantically searching for an answer to my question however none of my sources have clarity to the matter of hand. I would really love a clear explanation to: What exactly is Dark Matter? Please help me to have a clear understanding.
We don't know.
Though there are several ideas what dark matter could be, e.g. the humorously abbreviated WIMPs, all we know about dark matter is that is it massive (by light deflection, etc., etc.) and that it does not interact electromagnetically, and probably also not with the strong force. Other than that, there is no sufficently tested theory of dark matter to pronounce with confidence what it is. We only know what it is not (i.e. not EM charged, not strongly charged, and there are probably a few other constraints from observation).
Also, though highly unlikely, it could be that it is our theory of gravity, i.e. GR, that needs to be modified. In that case, it could be that there is no additional unknown matter, just different gravitational interactions from what we currently think.
"Dark matter" is just a name invented for the gravitational effects we see around galaxies and galaxy clusters. For example, the Milky Way has a "dark matter halo" that effects the orbit of the particles around the center of the galaxy. We can plot the orbits on a rotation curve. See this article: http://en.wikipedia.org/wiki/Galaxy_rotation_curve.
To agree with ACuriousMind, we know very little about this substance! The only way we know it even exists (which we are not completely sure of) is by its gravitational effects. Dark matter does not interact with light, since it does not reflect, absorb, or scatter light.
Dark matter is introduced into cosmology because Einstein's GRT does not correctly give the rotational speeds observed in galaxies, except to suppose that additional matter otherwise not observable would correct this.
Other cosmologies such as GEM (heaviside et al), give a correct explanation of this and therefore do not need a corrective fix.