Leaving a place you love is sad, but the speaker says that isn't the worst of it. The real ache comes from knowing the island will turn into a memory, and that the memory won't stay sharp. Other places and other experiences will slowly crowd it out.
The poem builds this feeling through repetition. Almost every line picks up the last word of the line before it: "sadness," "leave," "this beautiful island," "memory," "other memories." It feels like a thought circling back on itself, the way a mind does when it can't let something go. The opening question, "Do you know this feeling?", pulls the reader in and treats the emotion as something many people have shared.
The mood is quiet, wistful and a little resigned. Nothing dramatic happens. The speaker simply admits that even happy memories are not safe from time, and that loving a place means eventually losing the clear picture of it.