What is sanctification?

Sanctification is the work of God's free grace, whereby we are renewed in the whole man after the image of God, and are enabled more and more to die unto sin, and live unto righteousness.

2 Thessalonians 2:13 (NASB)
“But we should always give thanks to God for you, brethren beloved by the Lord, because God has chosen you from the beginning for salvation through sanctification by the Spirit and faith in the truth.”

Ephesians 4:24 (NASB)
“And put on the new self, which in the likeness of God has been created in righteousness and holiness of the truth.”

(ESV Global Study Bible Notes) 
“Sanctification refers to the transforming work of the Holy Spirit in a believer’s life, whereby the person becomes increasingly more like Christ.”