J'onn J'onzz has the ability to alter his density at the molecular level, which in practice allows him to become invisible, pass through solid objects (and vice-versa), or become invulnerably solid. An increase in his density results in a blue aura that increases his strength and invulnerability on par with that of Superman. This also allows J'onn to fully recover after sustaining severe physical damage, such as being torn apart.
In the comics, J'onn was a Manhunter, a Martian law officer and the (presumed) sole survivor of an engineered telepathic plague that wiped out the Green Martians. But this is not the case in the DC animated universe where J'onn J'onzz was the last Martian and one of the founding member of the Justice League. Check out J'onn J'onzz's natural Martian form HERE.
This is the JLU (Justice League Unlimited) J'onn J'onzz 5" (12 cm) action figure of the Martian Manhunter in his "invisible" state. If he was truly invisible, we won't be able to see him at all so we have to settle for this ;p