What is the significance of a long piece of red colored cloth in Superman's suit?
There is a (unreferenced) discussion of the costume and the cape here. In short, the cape is apparently meant to function as a pocket where he can keep items including his Clark Kent clothes.
(This seems a little funny to me, but that is what this guy, who may or may not be making it up, is saying. If anyone can find something that backs him up I'll edit and add it in. I haven't read the comics and I'm not intimately familiar with this part of his backstory, so for now this is the only in-universe answer I can find. Interestingly, the Superman wikia doesn't seem to have any detailed discussion of the costume or cape as far as I can see.)
Also, the "real life" rationale for the cape, according to Jerry Siegel as quoted in Superman: The Complete History by Les Daniels (via Wikipedia), is that they wanted to make the character as colourful and distinctive as they could. Not sure if this is what you're after, but hope it helps.