Star of David
The hexagram is often supposed to be an ancient charming symbol consisting of a triangle meaning ‘Water’ and another triangle meaning ‘Fire’. So much is certain in any case, that it is thought that the hexagram was on the shield of the Israelian king David (1010-970) and that is the reason why it is on the flag of present Israel. 
To the qualification of the emblem as ‘Shield of David’ or רּוֹרּ ךּגּמּ („Magen David”) little objections can be put. David is well known to have been one of the most belligerent kings of Israel (I & II Samuel) and a martial meaning of the emblem for that reason is obvious. The hexagram may be considered as a cypher of the first letter and last greek letters of his name: Δ and Δ (of „Δ[αβι]Δ”) united to a Y. This assumption would place the origin of the hexagram in the hellenistic era which began in Israel in the time of Alexander the Great (336-323) and was continued in the Ptolemy-era (323-30 BC). Probably not by coincidence the symbol also can be interpreted as the doubling of the Moabite letter or which also has the worth ‘D’.  This would reduce the period of the creation of the symbol to the era that Moab was a part of the Israelian monarchy (1020-723 BC).  Most likely however is that the symbol originates from the time of the Hasmonean and Herodian dynasties (166 BC-92 AD) because the kings of this dynasties bore greek as well as hebrew names and consequently were highly hellenized. For a long time however, the jews have used the latin as well as the greek alphabet so that a later era of origin is also probable. This is also suggested by the late appearance of the symbol, in itself a confirmation of the hypothesis that the star of David is in fact a greek monogram. 
Hexagram. 2nd-3rd century AD
Frieze from the synagogue of Kfar Nahum.
The symbol has undoubtedly a martial meaning and can be considered to have been a symbol of the jewish armed forces. This is also the opinion of several authors about the subject even when the common opinion is that the symbol has a magical or cosmological meaning. The martial meaning for the rest does not rule out the the magical meaning, nor the use that has later been made of it. The finding that the hexagram is a cypher of the name of David and has to be considered as a martial symbol in this way is more an addition than a contradiction of the current theories about the ‘shield of David’.
A consequence of this is that a six-pointed star, nor the pentagram can be considered to be graphic versions of the hexagram. On the contrary, these are better thought to be representations of the stars which are in the same relation to the sun as provinces to the empire.  Also, six-petalled flowers deserve no consideration as versions of a star of David.
In the time of the diaspora there cannot have been a jewish army but only jewish armed groups. For that reason the symbol usually is placed on movable objects and no representations are known where it is supported by angels or other supporters. 
The symbol could be used by all those accepting the religious authority of the Old Testament. For that reason it can be seen as a symbol of Jewish as well as of Christian and Muslim armed forces. In general however, the Christians preferred the XP-cypher and the Muslims the Sword of Islam as the symbol of armed authority.
The hexagram understood as the ‘coat of arms’ of king David can be considered to be the arms of his family up to Jesus as written in Matthew 1: 1-17: The Genealogy of Jesus the Messiah.  Consequently the hexagam can be also considered to be the arms of Jesus. This argument apparently is at the base of the use of the hexagram by the monophysites.
The monophysites separated from the main church at the Council of Chalcedon (451). The matter in dispute was the divine and human beings of Christ who, according to the monophysites were united after his incarnation into one single being but, according to what was decided by the Council, had remained two different qualities of him. The creed of Council about the matter was “Jesus Christ[...] has been revealed in two beings, without confusion, without change, without separation, without division and the difference between the beings is in no way annulled by the union.”
Monophysitism became at the Monophysite Schism the official docrtrine of the Syrian churches: the Jacobite-, the Armenian-, the Coptic- and the Etiopian churches. The hexagram appeared in the Middleages in the whole range of the monophysite churches (a narrow but united strip from the Black Sea to Ethiopia), reason why this symbol can be associated with this creed.
In the monophysite world the hexagram usually replaced the christogram.
The hexagram was a symbol of the Nubian eparchs and kings. It can be seen on the crown of Georgios II (969-979/1002) but it seems to be obvious to think that it was used befor. A continous use can be postulated because in modrrn times it was also displayed on the flag of the negus of Ethiopia but the lack of representations of high military officials of imperial Ethiopia does not encourage this hypothesis.
Later, on flag-charts of the 14th cenury, we see hexagrams at Libya and in Asia Minor and Armenia. A hexagram was also the emblem of the caliph of Morocco and, for unknown reasons, the emblem of Nigeria in the time of British rule.
Parapet Relief Slab.
Byzantine (Constantinople), 10th or 11th century. 
* This style of carving appears in 907 at the Church of the Virgin in the Lips Monastery in Constantinople. On the basis of parallels with the ribbon-lozenge design at the Church of Hosios Loukas, Phokis, Greece has been suggested as the place of origin.
Marble plaques of this kind were commonly used in churches to form the templon, which separated the sanctuary from the nave. 
** On this marble slab three symbols are united: in the middle is a 12-pointed sun-symbol which can be the symbol of the Byzantine Empire, two square crosses, symbols of the administrative authority and two hexagrams symbols of armed authority. The occurrence of both the symbols of adminsistrative- and armed authority can be explained by the fact that both authorities were combined in a Byzantine thema. The square crosses of a peculiar form may have been the symbol of the adminstrative authority of the thema Hellas where Phokis was situated. (H.d.V.)
© Hubert de Vries 2006-06-13. Updated 2014-02-27
 Oegema, Gerbern S.: The History of the Shield of David. Frankfurt a/Main, 1996.
 Faulmann, Carl: Das Buch der Schrift. Wien 1880/Nördlingen 1985, p.78.
 Today with the same name a part of Jordania east of the Death Sea.
 The oldest example quoted by Oegema is a stone frieze from the synagogue of Kfar Nahum (Kafernaum) from the 2nd or 3rd century AD (ill.)
 A pentagram in this way is better to be considered to be a symbol of Assyrian, Seleukian and Roman stadtholders in Palestine than as a Seal of Salomon.
 Also see: Oegema, op.cit. 1996. Angels were used in the jewish world in the same sense as elsewhere. For example there is a representation of a menorah, symbol of the jewish religious authority, supported by two angels.. (Illustrated in Rutgers, Leonard: Onderaards Rome.) In this way we have detected the symbols of the armed- and the religious jewish authority and also the symbol of the adminsitative authority which was probably the greek- or square cross.
 And also Luke 3 : 23-38 but he does not mention David as an ancestor of Jesus.
 Marble, 68.5 Î 80 cm. The Metropolitan Museum of Art, New York, N.Y. Fletcher Fund 1947 (47.100.47).
 Evans, Helen C. & William D. Wixom. Eds.: The Glory of Byzantium. Art and Culture of the Middle Byzantine Era A.D. 843-1261. The Metropolitan Museum of Art, New York, 1997. P. 38.