There is no such thing as a "Congressional Medal of Honor".
There is, however, a Medal of Honor. It is the highest award possible for military members, and is awarded by Congress after receiving nominations by the respective military chain of command.
In practice, the vast majority of nominations are downgraded to a "Service Cross", or silver or bronze star, before ever reaching the appropriate Congressional committee. This has caused some controversy in recent years, with most believing that the award has been inappropriately politicized, and with many in the pre-Congressional process downgrading nominations that do not "one-up" previous awards.
The stated requirements to be eligible for the Medal of Honor include "conspicuous gallantry and intrepidity at the risk of his or her life above and beyond the call of duty while engaged in an action against an enemy of the United States." Most are awarded posthumously, and there are few still-living recipients.
The Medal of Honor entitles the recipient to certain privileges, such as: a 10% increase in any pension; a lifetime monthly stipend above and beyond any pension or pay; special transportation privileges using DoD aircraft; and admission to any US Military Academy without regard to nomination or quota requirements for any children.
This list is not all-inclusive, and may have additions (but no subtractions) on a per-service basis.
Perhaps the most famous privilege of any Medal of Honor recipient, that of being entitled to a salute from any military member regardless of rank, is not an actual legal requirement, but is both highly encouraged and rightly deserved.