Beloved Son Beloved Child in Chinese / Japanese...

愛子 means “beloved son” in Chinese and Japanese.

While it could refer to a child in general (in Japanese), it's usually reserved or expected to be a title for a male child (in Chinese).

This can also be a given name in Japanese romanized as Aiko or Yoshiko.

愛の結晶 is a Japanese word that means the crystals or gems of love.

Figuratively, it means the treasures you create with your love (namely, your children). Some will translate this as “fruit of love.”
It's also kind of a nickname for your beloved children.