Colossians 2:9 (LSB)
9 For in Him all the fullness of Deity dwells bodily,
This verse teaches that Jesus Christ possessed the entire Essence of God in hypostatic union with a human nature.
A similar statement to the one made in this passage, and its close parallel in Colossians 1:19, is made with respect to believers in the book of Ephesians:
Ephesians 3:19
19 And to know the love of Christ that surpasses knowledge, so that you may be filled with all the fullness of God.
The above statement can be understood in light of the New Testament doctrine that believers are the Temple of God, in which He places His Holy Spirit (Romans 5:5, 8:9: 1 Corinthians 3:16-17, 6:19-20: 2 Corinthians 1:21-22, 5:5, Ephesians 1:12-14, 4:30: 2 Timothy 1:14). With respect to Jesus, He was given the Spirit of God without measure (John 3:34, Acts 10:38), and so it is all the more fitting to apply these statements to Him, and even to say, as the passage in question says, that the "fullness of Deity dwells bodily" in Him.