Charlie was conceived largely by accident due to Amenadiel not knowing it was possible for an angel to impregnate a human woman. Linda suffered from fainting after she and Amenadiel broke up, with Maze forcing her to go see a doctor. Learning that she was pregnant, Linda had the complete support of Amenadiel and Maze despite their lack of knowledge about babies or angel babies, for that matter.
Shortly after Charlie's birth, he was kidnapped by Dromos and the demons who were hoping to make him the new King of Hell. However, he was rescued and returned to his parents.
Nephilim Physiology: Charlie is a divine angel-human hybrid, also known as a nephilim, the first of his kind. Being half-angel, Charlie can be taken to and from Earth without dying. In "Orgy Pants to Work", Remiel said that she had to take him to Heaven "for all eternity." This indicates that, as a half-angel, Charlie is immortal. Remiel also states that she was able to sense his celestial nature from within the womb. As a half-angel, Charlie is also able to rule Hell. However, Charlie later contracts a cold and is also shown to be frozen in time due to Amenadiel's powers, putting his celestial status into question (although, it may be because he is just a baby, or that Michael somehow caused this to get to Amenadiel by exploiting and manifesting Amenadiel's fears).
Some of the other suggested names for Charlie were Zoriel, Zori, Ezekiel, Zek, Jack, Jackiel, Azmortiel, and Michael.
Jack is the name of the nephilim Jack Kline, who is the son of the archangel Lucifer in the TV series Supernatural.
Michael is presumably a reference to archangel Michael, which would explain why Amenadiel promptly disregards the name as a possible choice.
Nephilim are mentioned in Genesis 6:4.
Despite Charlie being half-Angel, he is still apparently (see above) a mortal as when Amenadiel stopped time, only the mortals were affected but not the celestials (Lucifer, Amenadial, Maze and Michael).
Charlie is fascinated by his uncle Lucifer's devil face, which is one of the few ways to calm him down.