Of course it is not real carp(Carp is "Koi[鯉（こい）]" in Japanese.). Its body is made of cloth and it is called Koi-nobori[鯉のぼり（こいのぼり）].
Koi-nobori is displayed for children's health, growth & success in the garden on Tango no Sekku[端午の節句（たんごのせっく）]. Koi-nobori is a Japanese original custom but derived from a Chinese legend that the carp swimming up rapid stream of Longmen[龍門] River become dragon. This story is known as an allegory of the advancement.
In the Edo Period(1603--1868), Samurai's families displayed banners or floats with a family crest in front of the gate on Tango no Sekku.
In competition with them, citizens begun to display floats with painted Koi. It is the origin of Koi-nobori.
Hiroshige Utagawa, "Suidobashi-Surugadai from 100 Famous Views in Edo[江戸名所百景 - 水道橋 駿河台（すいどうばし するがだい）]":
With Koi-nobori, hanging banners or floats are seen in this picture.
Generally, It is said that biggest black carp is a father(Magoi[真鯉（まごい）]), red one is a mother(Higoi[緋鯉（ひごい）]) and small one is a child today.
From April to May 5, Koi-nobori festivals held throughout Japan. In Kazo[加須（かぞ）] City, Saitama Prefecture where is the largest production area of Koi-nobori, a huge Koi-nobori with 100 meters long swims in the sky. In Tsuetate Hot Spring[杖立温泉（つえたておんせん）], Oguni[小国（おぐに）] Town, Kumamoto Prefecture, about 3,500 Koi-noboris are hanged across the Tsuetate River through the hot spring town.
Koi-nobori at Tokyo Tower in Minato, Tokyo