Superman's costume (and those of the other Golden Age superheroes) were inspired by the circus performers of the day which sometimes included a cape. When Siegel and Shuster designed the costume the added the cape and the look became so iconic no-one ever removed it from the design but this you probably know.
Within the context of the story the reason Martha Kent added the cape was simply because it looked good when he flew. I don't have a concrete example of a time she did this in the comics but if you watch the pilot episode of Lois and Clark you'll see what I mean.
Before Crisis on Infinite Earths Superman's costume had been made out of indestructible baby blankets from Krypton (I assume there was a high infant mortality rate on their planet) which Martha was somehow able to cut and stitch with Earth instruments. But in the updated version of Superman's origin that followed it was revealed that Superman's body creates an "electromagnetic aura" about half an inch from the surface of his skin. Not only does this aura protect him but it also protects all clothing that falls within it and even prevents them from getting dirty, thus this became the new in continuity reason for why Superman wears tights but there was no reason he'd have a cape as it fell outside the aura and would get damaged easily and Superman needed Martha Kent to make large numbers of replacement capes. So the writers explained the reason he had a cape was because it had a pouch for his Clark Kent clothes, even though there was no protection and it would have probably been a better to leave them in a bag of some sort the way Peter Parker does. The cape with a pouch was actually an idea that itself had been introduced sometime in the 1950s.
In later years the origin was updated again and in the new version Martha had seen holograms of people from Krypton wearing capes and decided to make Clark a Kryptonian set of clothes as it was part of his heritage and for this she added the cape.
In the New 52 it turns out that Superman's costume is a Kryptonian ceremonial armour that Superman stole from Brainiac who himself stole it from Krypton possibly from Jor-El as he's seen wearing it. The suit adapts to whoever wears it and can change colour, before Superman wore it it was white with a circle on the chest and when he wore it and time travelled into the past of Krypton it changed to green with a planet logo on his chest. The suit can even shrink to just the logo so Superman can carry it around during the summer. But the cape was apparently a baby blanket or piece of cloth that Jor-El and Lara sent with baby Kal-El to Earth which Superman has a hard time parting with for some reason and even wore it with his early costume which was just a t-shirt and a pair of jeans! The cape is now like a security blanket which makes Superman like Linus from the Peanuts comics!