Come, ye thirsty, come, and welcome,
God's free bounty glorify;
True belief and true repentance,
Every grace that brings you nigh.
I'm going to take a stab at this stanza, but you can feel free to give me your thoughts (as I'm a little confused on some of the wording).
Overall, the theme is to go to Christ. What I love is that this passage merges the doctrinal truths of God's sovereign grace and our joyful responsibility. Jesus commands and bids us to come to him. He pleads with sinners - people who don't love Him - to find satisfaction in Him. Yet, the only way we really will arrive at home with Him are by the graces of true belief and repentance. Belief and repentance are God's gifts to us! Praise God and never cease to be amazed that He has called you as His child and given you the ability to trust and turn to Him!
Now, on to the second line. We are to come to Christ and welcome the blessings that flow. This seems to somewhat fall in line with Hebrews 11:6 where we find that faith must believe that He is a rewarder of those who diligently seek Him. Those who truly believe in Christ trust that He'll reward them. So, they welcome the blessings of God's grace. Hence, they glorify God's free bounty. In other words, when a sinner repents and trusts in Christ - acknowledging their need of grace, God's beauty and wonder is seen in greatest splendor!
Remember Romans 5? Where sin abounds, grace abounds all the more! When people (whether moral or immoral people) come to Christ, welcome His bounty, God is truly glorified.
So, even if you are a believer, where do you find yourself today? Do you find yourself thinking that your imperfection keep you from God? It's true that it can. But, would you instead acknowledge your sinfulness and trust in a Savior that desires to reward you with His great grace? And, as a result, He ends up getting all the glory, and you are blessed with His good!