The Swallow as a Christian Symbol represents the Incarnation of Jesus and the Resurrection, as it appears every spring to announce its arrival.
The Easton Bible Dictionary provides the following definition, meaning and emblem for the Swallow Christian Symbol in the Bible.
(1.) Heb. sis (Isa. 38:14; Jer. 8:7), the Arabic for the swift, which "is a regular migrant, returning in myriads every spring, and so suddenly that while one day not a swift can be seen in the country, on the next they have overspread the whole land, and fill the air with their shrill cry." The swift (cypselus) is ordinarily classed with the swallow, which it resembles in its flight, habits, and migration.
(2.) Heb. deror, i.e., "the bird of freedom" (Ps. 84:3; Prov. 26:2), properly rendered swallow, distinguished for its swiftness of flight, its love of freedom, and the impossibility of retaining it in captivity. In Isa. 38:14 and Jer. 8:7 the word thus rendered ('augr) properly means "crane" (as in the R.V.).