Snazzy means 'well put together, or well turned out (dressed)," for example, "You look snazzy," or, "That's a snazzy outfit." Songs take liberties in order to make rhymes, so the word has been shortened to snazz, to rhyme with jazz, and it indicates someone well put together or well-dressed.

The song is saying people are showing off (parading) their material possessions (snazz) as though that makes them something special. The song is stating that people are living in ignorance without realizing what's really going on in society - especially the pain of the less fortunate.

Parade can mean display or show off, and it does seem to in your lyric. I hadn't heard "snazz", though it looks like it might be related to "snazzy", and it turns up online. This one gives "fanciness": http://onlineslangdictionary.com/meaning-definition-of/snazz Snazzy will get you "stylish and attractive." https://www.urbandictionary.com/define.php?term=snazzy Lyricists will bend any sounds or meanings in search of a rhyme, a rhythm, a feel ;)