game preserve, pasture, garden
囿 centers on an enclosed natural space for animals or plants: a game preserve, pasture, or garden. The common thread is a bounded area where living things are kept or cultivated.
囿 combines 囗 (enclosure) with 有 (to have, exist), suggesting a bounded area where animals or plants are kept. The exact historical development is uncertain, but the component structure fits the meaning of a preserve or garden.
An enclosure 囗 with 有 (to have) inside: picture a fenced area where you have animals or plants, like a game preserve or garden.
For ユウ, imagine you walking through a peaceful garden enclosure: you -> ユウ, and the garden is a place you have.