Ascending the mountain of the Lord is symbolic to coming in to His glorious presence. The psalmist instructs us on what is required by God to stand before Him. As sinners we have separated ourselves from a holy, pure, and righteous God.We must go through the "cleansing" process.
Thanks to Jesus' atoning sacrifice on the cross our sins can be forgiven. You have probably sang the song inspired by this psalm as a request to God. Give us clean hands, give us a pure heart, and not let us lift our souls to another.
Pure hands represent our outer sins, things we do (and others can see) that dishonored God. Clean hearts deals with what goes on inside us (what others cannot see) our thoughts, feelings, forgiveness,etc. Our souls to an idol reminds us to keep the the first four commandments. We must keep God first and foremost in our hearts, minds, body, and soul. Love Him with all your being.
Make this your desire and song of your heart. Amen?