Seven is a number frequently used in the Bible to describe holy things. For example there are seven Christian gifts listed by Paul in Romans 12. In Revelation there are seven churches, with seven messengers given the words of Christ. Also in the book there are seven seals, seven plagues and seven claps of thunder described. The final resurrection is said to take place after the sound of the seventh trumpet.
The Holy Spirit Himself is called “the seven Spirits of God” (Revelation 1), giving the number a symbolic meaning. Seven = Perfection.
The beautiful pure-white swan, depicted seven times over, illustrates the perfect, Divine Majesty of God. It is that perfection that we, sinful people offend with our transgressions, and return to thanks to the blood of Christ.
Without Christ, we’re ugly ducklings, doomed to eternal misery. Through Christ we can be washed and made white (Revelation 7), dwelling with God for all of forever.