I don't remember where I got the notion, but when I think about songs I like to think in terms verse and poetry, in addition to the strictly musical. (I normally do this thinking in Swedish, but I hope these terms capture what I mean) These are related but distinct concepts, and in the words sung to music you will likely find at leas one, and often to some extent both.
Verse, in this context, concerns the sound of the words and disregards their meaning. It's the meter, the rhymes, the patterns of syllables that work together. Good verse is an art form aimed at pleasing the ears, not the mind.
Poetry, on the other hand, concerns the meaning of the words. It's a mater of what is said with what words, of the metaphors, the figurative descriptions. The ambiguities and the implications of what is said. While good verse pleases the ears, good poetry pleases the hart and the mind.
Neither of these are exclusive to song lyrics, they could just as well apply to spoken words, but I'd say song lyrics necessarily contain at least one of them. There are great lyrics where the rhymes are sparse and the syllable count in the lines seems completely random, but where the beauty of the words draw tear to your eyes and you feel like a wiser person after hearing them. Poetry.
There are also great songs where the meaning of the words is totally insignificant, but they sound very good. It's the catchy alliterations, the perfect flow of syllables in many rap songs, the clever rhymes. You could even listen to a song in a language you don't even understand, and find yourself repeating parts of the lyrics that stick. These are also among the first things children start appreciating about lyrics. Some might say this hints at it being a childish, cheap or mundane quality, but you could also argue it's a sigh that the beauty of the words is something really deep in our minds. This is verse.
When you write lyrics of your own, you can aim for one or the other. You could even aim for both. You don't need to aim that high either. In any case, I think it's worth while giving these two notions a thought. If nothing else to see that quality is not measured one-dimensional scale, and that there's more than one direction to aim when you want to write good lyrics.