Grace is "energy" integral to angels. It is essentially what differentiates an angel and a human, both having a mortal spirit. If an angel removes their grace, they are either rendered mortal within their vessel or, if they are not using a vessel, are reborn to human parents in their own body.
Grace supplies angels access to enochian magic, which is how they use their power, without it, they would be rendered powerless. Depending on how the grace is removed, the celestial being may retain a little of its power, such as telepathically hearing other angels communicating. If Grace were combined with a human soul rather than an angelic spirit it would create a Nephilim, which are more powerful than angels. These beings can be created when angels and humans reproduce together, combining soul and grace.
Grace is a type of energy angels are infused with. It resembles a shining bluish-white mist.
It appears that all angels are endowed with their own grace. This includes not only average angels such Joshua and Theo, but also seraphim such as the "new and improved" Castiel. Therefore, it can be assumed that other types of angels, e.g. Cupids and archangels, also have grace. When not infused in an angel, grace must be stored in a vial or it will fall to Earth. Humans who see falling grace may mistake it for a meteorite. Where grace touches down on Earth, it vastly enriches its surroundings rather than destroys them; the presence of Anna's grace caused a barren field to flourish with vegetation and the spot where it landed created a massive oak tree that looked as though it were centuries old in the space of six months. It is suggested that Anna's grace resided in this tree until it was taken by Uriel.
Grace is the source of most of angels' power, endowing them with Enochian magic, including immortality and teleportation. However, angels who had their grace removed may still be able to tap into varying powers, including the ability to tune into "angel radio", Supernatural Perception, and telekinesis.
So long as a vessel is possessed by an angel, that vessel also contain that angel's grace. Even after an angel departs from his vessel, a portion of his grace lingers within that vessel. Containing traces of an angel's grace does not harm the human in question and may even help them, as Castiel notes that Gadreel's grace was keeping Sam Winchester mostly healed from the Trials of God. Once Castiel removed this grace, Sam fell ill once more.
While possessing Adina's grace, when Castiel retrieved what was left of his own grace (a portion of it was used in Metatron's spell), he became a Seraph once again but his powers weren't completely restored and his wings were damaged. It is unknown if this was a result of Metatron's spell or the amount of the grace that was left.
Though it is agonizing for the angel, it is possible for an angel's grace to be removed, either voluntarily or by force and in either vessels or in their true forms. It is viewed as a serious crime for angels to remove their own grace, one that requires the angel in question to be punished either via execution or imprisonment and torture. Anna even compared it to first-degree murder for humans. It is unknown whether or not the forcible removal of grace is viewed in a similar light, although it would seem so as Castiel was disgusted with himself when he did it to Theo, calling it "barbaric."
Angels who lose their grace fall to Earth and essentially become humans. If the angel in question is possessing a vessel at the time they lose their grace, they are then locked into their vessel until death. If, however, the angel does not have a vessel, they are reborn to human parents through a human body of their own. In the case of Anna Milton, who was reborn with her own body, she gradually lost her memories of being an angel as she grew up human, but it is unknown if she deliberately repressed her memories or if this happens over time to all angels who lose their grace. Regardless, angels who lose their grace become subject to human emotions, urges, and weaknesses. Other angels may still recognize an angel who has lost his grace, but will be able to tell that he is no longer truly an angel.It is also possible for angels who have lost their grace to regain it in order to restore their angelic power and status. They can use either their own grace (if they can find it) or remove the grace of another angel and use it for themselves. The effects of an angel absorbing another angel's grace are unknown—specifically, whether the angel regains all of his original powers or that of the other angel's. However its revealed that using another angels grace for to long will cause the grace to burn out and kill the angel in question, although the exact time line is unknown. Whether or not any other creature can also absorb grace is also unknown. The absorption of grace is a potentially dangerous process for humans and demons: when Anna absorbed her grace, she frantically warned Sam, Dean, and Ruby to close their eyes, and a powerful demon who did not heed her warning had his host body disintegrated in the ensuing blast. Castiel and Uriel, however, were able to watch without harm. Absorbing her grace caused Anna's body to glow white, her eyes to glow yellow, and her body to soon disintegrate in a burst of white light, requiring her to call in favors to have it restored for her to use as a vessel. Castiel's absorption of Theo's grace did not cause a similar reaction. It is unknown what happens to the angel's soul when he reabsorbs grace, although that Anna specifically feared the prospect of losing of her human emotion by regaining her grace may indicate that the angel loses his soul by regaining his grace. However, Anna seemed to continue feeling emotions, thus causing many to believe that the soul remains within the angel.
An angel's grace is the third part of the spell to banish all the angels. Metatron removes Castiel's for the spell by slitting his throat and collecting his grace in a vial. He later claims to Hannah that there is some left, indicating that he didn't use it all up for the spell. This is shown to be the truth in Book of the Damned when Castiel locates his remaining grace inside a book in a library. Reabsorbing it, combined with the grace he took from Adina restores Castiel's full power and Seraphim status.
The Men of Letters theorized that an angel's grace could be used to locate that angel through a tracking spell, but did not live to test their theory. The spell requires a sufficient amount of grace, extracted and collected with a special syringe. Sam and Castiel tried to track Gadreel this way, but did not use enough grace in the spell for it to work.