Yume is written with the kanji 夢.
It is a kanji derived from the word « ime » (寝 目) where 寝 means here « sleep » and « see ».
Originally, the dream is what you see when you sleep. A psychic projection from sleep. But this is also what we want to achieve in the near or far future.
The dream, from sleep to aspiration
Towards the Heian period (794-1185), it began to be used with a figurative meaning, that is to say for something fragile, uncertain.
Jinsei ha yume da (人生 は 夢 だ), thus means « life is uncertain » because it is unstable and can stop at any moment, like a dream.
It is only from the modern era that Yume is used to indicate something that we plan to achieve in the future.
Watashinoyume wa Okinawa no karate or renshū suru kotodesu
私 の 夢 は 沖 縄 の 空手 を 練習 す る こ と で す.
We can find this meaning of the dream as ideal in the Manga shenen (少年) where the main hero clings to the end to achieve its ambitions.