Is it permissable/proper for a male Chtistian to wear a kippa, and could you explain its intended use and origin?
The Talmud states that a number of Sages used to cover their heads, in respect of the Divine Presence (Shechinah) above them (Kiddushin 31). Elsewhere, the Talmud writes that convering one’s head protects a person from sin, describing how a person who by nature would have been a thief, was protected from his fate by virtue of his covering his head as a child (Shabbos 156). Concerning Jewish Law, some authorities maintain that there is an obligation for men to cover their heads, whereas others write that doing so is virtuous, but not obligatory.
Note that even authorities who write that there is no obligation to wear a kippa, write that one must do so when entering a Shul (see Magen Avraham, Orach Chaim 91:3), or when reciting blessings (Kol Bo 11; or Zarua 2:43; Tur, Orach Chaim 8; Taz 8:3).
For non-Jews, there is no obligation to cover one’s head, and indeed, one renowed authority (Chasam Sofer) writes it is the “way of non-Jews” to have the head uncovered. However, there is certainly no prohibition in covering the head with a kippa, and if one wishes to do so, with a view to honoring the Divine Presence above us, or to instilling within himself fear of Heaven, it would be considered worthy conduct.
Sources: concerning the obligation, or otherwise, to wear a kippa, see Kol Bo 11; Tashbatz 549; Maharshal 72; Darkei Moshe 2:3; Magen Avraham 91:3; Biur Ha-Gra 8:6; Bach 2; Birkei Yosef 2; Chasam Sofer, Choshen Mishpat 191.