56:8-9 David was confident that God knew about all his experiences intimately. He knew wherever David had gone and had made note of all his painful sufferings. The psalmist asked God to remember his sufferings in a graphic way. He wanted the Lord to store his tears in His skin bottle so their volume might move Him to act for David.
56:10-11 These verses rephrase the refrain to this song that appears in verse 4. The refrain is a strong affirmation of David's confidence in God.
56:12-13 As in other psalms, David spoke of his future deliverance confidently as though God had already given it to him. The vows to which he referred were those David had made to God. He had promised to praise Him with thank offerings after God delivered him from his enemies.
The believer who is doing God's will can confidently appeal for His aid when evil people oppose him. Remembering that our Helper is the Lord of all and that our opponents are only mere mortals will strengthen our faith.