To summarize their story basically, their parents came to rare encounter with a Darkrai. After that night their mother fell very ill and was getting endless nightmares which was deteriorating both her mind, psyche and overall health. The family was looking for a cure for this and were told the only solutions was to find the legendary Pokemon Cresselia or it’s feathers called lunar Wings

Considering people go through their entire lives without encountering legendary Pokemon they settled on finding the lunar wing which seems more obtainable. So they built a boat and set off to sea in search of it.