St. Michael the Archangel is depicted in a number of ways, but most often he is wielding a sword, striking down Satan.
Normally this sword is made of metal, but often it is a flaming sword, both in Eastern icons and Western statues.
The primary reason for this flaming sword is the tradition that whenever an angel is not mentioned by name in the Old Testament, it is St. Michael.
According to the booklet St. Michael the Archangel, "St. Ambrose says that God commissioned St. Michael to lead Adam into Paradise, to explain to him the purpose of his creation, to guide him and to associate with him in visible form. After the fall of Adam and Eve, this same glorious Archangel stood guard at the gate of Paradise with flaming sword, 'to keep the way of the tree of life.' (Genesis 3:24)."
However, the text of Genesis seems to suggest that a "cherubim" guarded Paradise, not an "archangel," "He drove out the man; and at the east of the garden of Eden he placed the cherubim, and a flaming sword which turned every way, to guard the way to the tree of life" (Genesis 3:24).
Nevertheless, St. Michael was often seen as the "Guardian of Israel," and was even said to be the angel that protected them from the Egyptians through a "pillar of fire" (cf. Exodus 14).
The flaming sword could also symbolize the reality that angels are spiritual beings and their war is not with "flesh and blood," but with spiritual foes.
The next time you see St. Michael holding a flaming sword, know there is much history and symbolism in the depiction.