We should seek to live pure lives because to do so glorifies God. It honors Him. Not simply morality, being nice, etc., but pleasing God because you love Him and want to honor Him.
God wants you to keep your ways pure. How? He wants you to live according to His word. Seeking Him with all of your heart, hiding His word in your heart, and meditating on God’s precepts.
Here is a great purity test for both married and single people: If a complete stranger saw how you are relating to someone who is not your spouse, would they think you are married to that person? Something to consider in light of Psalm 119:9, especially since nothing is hidden from the Lord.