The word resolved itself means determined. So if you replace resolve with determine, you would get, "I am DETERMINED no longer to linger - charmed by the world's delights. Things that are higher, things that are nobler - these have allured my sight."
This world has so many "charms and delights" that can lead us astray. Hebrews warns us in chapter 11 that sin is pleasurable for a season and Proverbs 16 warns us that the end of sin is death! We need to be having our "sights allured" by the things above. As Jesus tells us in Matthew 6, we need to make sure we're placing our treasures in Heaven above.
The song also says, "I am resolved (determined) to go to the savior, leaving my sin and strife." We should have no desire to live in sin because it is something that separates us from God! We should not be a slave to sin - but rather, leave it behind and GO to the savior!
The last verse of the song talks about following the savior and being faithful and true each day. Christianity isn't about following Christ when we feel like it, it's about doing it each and every moment of our life. Be determined to follow the savior everyday of your life.
Hopefully you've gained a little bit from these thoughts today and hopefully you will sing this song differently from now on.