It really means Christ-likeness - reflecting the character of Christ in our character.
In Genesis 1:26, we read that we are created in the image of God. This means we were created to be in relationship with God and we were created to reflect God in our relationships with others.
Jesus showed us while He walked this earth what it looks like to live as who we were created to be: in the image of God, living in relationship with the Father and reflecting His character in relationship with others.
The Son radiates God’s own glory and expresses the very character of God. Hebrews 1:3
Jesus is still showing us what it means to live as who we were created to be through the work of His Holy Spirit in our hearts and minds. The Holy Spirit teaches and reminds us of who Jesus is, what Jesus says, and who we are in Christ.
When the Father sends the Advocate as my representative - that is, the Holy Spirit - he will teach you everything and will remind you of everything I have told you. John 14:26
Reflecting Jesus, living in holiness, growing in Christ-likeness - these are important aspects of our identity in Christ - and of being confident in that identity - because they speak of transformation, a true change of who we are, from the inside out.
They speak not only of who we are in Christ, but who we are becoming in Christ.