It is Christ's desire that each of his children be transformed into his likeness and receive his image in their countenances. This process requires a mighty change and a new birth. We literally become new creatures in Christ.
In the insect kingdom, a complete metamorphosis would be analogous to a caterpillar changing to a butterfly.
Allen Meyer wrote the quote used below about an incomplete metamorphosis:
Insects have life-cycles that are very short so we can watch and learn from the birth, growth, maturity, and death of an entire generation in only one year. They develop in a very unique manner that follows one of two basic paths: complete and incomplete metamorphosis. These help us understand the two most important paths of all: Christ’s and Satan’s (Genesis 3:15).
Incomplete metamorphosis involves the gradual change from a newly hatched juvenile to a fully formed adult. The juveniles resemble the adults, and one usually calls them nymphs (Greek for “young, veiled bride”). The nymphs go through a series of moults without any dramatic change in appearance, except they may have wings when they become adults. This occurs in insects such as termites, lice, locusts, and dragonflies (Revelation 9:9). It’s sort of like a serpent when it sheds its skin; same critter, a little older, with a new outfit.
This process is well-described by the Greek word metaschematizo. It means “to change shape” or “to disguise,” from schema, a “figure” or “external condition” (compare “scheme” or “schematic”). Metaschematizo is translated “transform” in 2 Corinthians 11:13-15 —
For such are false apostles, deceitful workers, transforming themselves into the apostles of Christ. And no marvel; for Satan himself is transformed into an angel of light. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works.
Satan is the chief copier, and will even copy Christ (Matthew 24:24-31; 2 Thessalonians 2:3-4). He changes his skin from time to time, but he’s the same, old critter underneath; as with his ministers. Their works are evil, and haven’t changed since the beginning; just as adult locusts are larger, winged versions of young locusts (2 Corinthians 11:2-4).
(Meyer, Allen R., Insects and Other Critters of the Bible, Bible-Student Resources, Claimont, Alberta, Canada, 1997, pg 150)