If segmentals are the letters, words and phrases, suprasegmentals are the music.
For instance, the words "how are you today?" can be divided into segments; but the way I say "how are you today?", e.g. the rhythm and intonation, is suprasegmental.
If you learn English simply to read, suprasegmental features are of little importance. If your job requires you to understand the expressive aspects of spoken English, on the other hand (if you work on a helpdesk, for instance), they are probably of very great importance.