In Exodus 4:18, this signifies the continuation of the previous life. (Arcana Coelestia 7014)

In Exodus 13:17, this signifies to fall into falsities. (Arcana Coelestia 8097)

In John 13:3, this signifies to be conceived and to exist from the Divine in Himself, and to be united to Him as soul to body. (Arcana Coelestia 852[9])

The number three in the Bible represents completeness. That's why Jesus rose on the third day after the Crucifixion -- his transformation was complete. It's why Elijah stretched himself on the dead child three times, why Jonah was in the belly of the fish for three days, why the Lord called Samuel three times, and many more. It's also reflected in the fact that there are three levels of heaven, three levels of hell, three levels to human life and, ultimately, three aspects of the Lord Himself: Father, Son and Holy Spirit.