From Wikipedia:
The "Passion" in "passion flower" refers to the passion of Jesus in Christian theology. In the 15th and 16th centuries, Spanish Christian missionaries adopted the unique physical structures of this plant, particularly the numbers of its various flower parts, as symbols of the last days of Jesus and especially his crucifixion:[32]
Blue passion flower (P. caerulea) showing most elements of the Christian symbolism

The pointed tips of the leaves were taken to represent the Holy Lance.
The tendrils represent the whips used in the flagellation of Christ.
The ten petals and sepals represent the ten faithful apostles (excluding St. Peter the denier and Judas Iscariot the betrayer).
The flower's radial filaments, which can number more than a hundred and vary from flower to flower, represent the crown of thorns.
The chalice-shaped ovary with its receptacle represents a hammer or the Holy Grail.
The 3 stigmas represent the 3 nails and the 5 anthers below them the 5 wounds (four by the nails and one by the lance).
The blue and white colors of many species' flowers represent Heaven and Purity.